Method and apparatus for calculating thermal stress and thermal strain of CORC cable, computer device, computer-readable storage medium, and computer program product
By obtaining the inner and outer surface temperatures of CORC cables and using thermal balance and stress-strain equations to calculate thermal stress and thermal strain, the problem of inaccurate assessment of low-temperature shrinkage of CORC cables in existing technologies is solved, providing a simplified calculation method and scientific basis.
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- CHINA THREE GORGES CORPORATION
- Filing Date
- 2025-07-29
- Publication Date
- 2026-07-02
Smart Images
Figure CN2025111205_02072026_PF_FP_ABST
Abstract
Description
A method, apparatus, computer equipment, computer-readable storage medium, and computer program product for calculating the thermal stress and thermal strain of CORC cables.
[0001] Cross-reference of related applications
[0002] This application claims priority to Chinese Patent Application No. 202411911874.2, filed on December 23, 2024, entitled "A Method and Apparatus for Calculating Thermal Stress and Thermal Strain of CORC Cable", the entire contents of which are incorporated herein by reference. Technical Field
[0003] This application relates to the field of superconducting cable technology, specifically to a method, apparatus, computer equipment, computer-readable storage medium, and computer program product for calculating the thermal stress and thermal strain of CORC cables. Background Technology
[0004] Based on the fundamental properties of superconducting materials, superconductors must operate below their critical temperature to exhibit superconductivity. For superconducting power technology, superconducting power devices generally operate below 77K (Kelvin) in the liquid nitrogen temperature range. From room temperature to the superconducting operating temperature range, the superconducting materials themselves, as well as the related functional components and structural components of the device, will be subjected to thermal stress and thermal strain caused by the low temperature.
[0005] As one of the most widely used superconducting power devices, superconducting cables exhibit significant low-temperature deformation during long-distance power transmission. Without assessing the stress and strain of superconducting cables at low temperatures, and without taking measures to compensate for the low-temperature shrinkage, the cable core will bear substantial thermal stress, potentially damaging the conductors and insulation structure, leading to ignition failure or even burnout. Therefore, calculating the thermal stress and strain of superconducting cables, especially CORC (Conductor on round core) cables with their high heat exchange efficiency, flexibility, electromagnetic environment friendliness, and widespread use, is of great value for the application and protection of superconducting cables.
[0006] However, the inability to reasonably analyze and calculate the thermal stress and thermal strain of CORC cables leads to an inaccurate assessment of the degree of low-temperature shrinkage of superconducting cables. Summary of the Invention
[0007] In view of this, this application provides a method, apparatus, computer equipment, computer-readable storage medium, and computer program product for calculating the thermal stress and thermal strain of CORC cables, in order to solve the problem of the inability to reasonably analyze and calculate the thermal stress and thermal strain of CORC cables.
[0008] In a first aspect, this application provides a method for calculating the thermal stress and thermal strain of CORC cables, the method comprising:
[0009] The inner and outer surface temperatures of the core of the CORC cable are obtained. Based on the inner and outer surface temperatures of the core, the steady-state radial temperature distribution of the core is determined using the heat balance equation of the CORC cable.
[0010] The Young's modulus, Poisson's ratio, and coefficient of thermal expansion of the core functional layer are obtained. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, and coefficient of thermal expansion, the thermal strain of the CORC cable is determined using the stress-strain balance equation of the CORC cable. The thermal strain of the CORC cable includes radial strain, circumferential strain, and axial strain.
[0011] Based on the thermal strain of CORC cables, the thermal stress of CORC cables is calculated using the stress-strain relationship; the thermal stress of CORC cables includes radial stress, circumferential stress, and axial stress.
[0012] This embodiment provides a method for calculating the thermal stress and thermal strain of CORC cables. Based on the inner and outer surface temperatures of the cable core, the steady-state radial temperature distribution of the cable core is determined using the thermal balance equation of the CORC cable. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, and coefficient of thermal expansion, the thermal strain of the CORC cable is determined using the stress-strain balance equation of the CORC cable. Based on the thermal strain of the CORC cable, the thermal stress of the CORC cable is calculated using the stress-strain relationship. This method achieves a reasonable analysis of the thermal stress and thermal strain of CORC cables, avoiding the complex modeling and analysis steps and time-consuming calculation process of numerical simulation methods. It can reasonably reflect the degree of low-temperature shrinkage of CORC cables and has a simplified solution process, providing a portable and effective method for compensating for low-temperature shrinkage of CORC cables, taking into account both technical significance and engineering practical value.
[0013] In one optional implementation, the steady-state radial temperature distribution of the cable core is determined using the CORC cable thermal balance equation based on the inner and outer surface temperatures of the cable core, including:
[0014] Obtain the inner and outer surface temperatures of the CORC cable core, and calculate the heat flux at the core radius based on the inner and outer surface temperatures of the core.
[0015] The steady-state radial temperature distribution is determined based on the heat flux at the cable core radius.
[0016] This embodiment provides a method for calculating the thermal stress and thermal strain of CORC cables. It calculates the heat flux at the cable core radius using the inner and outer surface temperatures of the cable core, thereby determining the steady-state radial temperature distribution. The method derives the function of temperature versus radius using the CORC cable's thermal balance equation, neglecting the effects of air gaps between superconducting tapes, semi-overlapping processes, AC losses in the conductor layer, and viscous losses in the convective heat transfer surface. This method reasonably reflects the structural characteristics and application conditions of CORC cables and is easily solvable, providing a scientific basis and effective means for assessing the low-temperature shrinkage of superconducting cables.
[0017] In one optional implementation, the heat flux at the cable core radius is calculated based on the inner surface temperature and the outer surface temperature of the cable core, including:
[0018] Obtain the surface parameters of the core functional layer, and calculate the heat flux at the core radius under the Dirichlet boundary conditions based on the core inner surface temperature, core outer surface temperature, and core functional layer surface parameters.
[0019] Alternatively, obtain the heat transfer coefficients of the inner and outer surfaces of the cable core, and calculate the heat flux at the radius of the cable core under mixed boundary conditions based on the inner and outer surface temperatures of the cable core, the surface parameters of the functional layers of the cable core, and the heat transfer coefficients of the inner and outer surfaces of the cable core.
[0020] This embodiment provides a method for calculating the thermal stress and thermal strain of CORC cables. By calculating the heat flux at the core radius under Dirichlet boundary conditions and mixed boundary conditions, it achieves accurate calculation of the heat flux at the core radius under different CORC cable application scenarios.
[0021] In one optional implementation, the thermal strain of the CORC cable is determined using the stress-strain balance equation of the CORC cable based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, and coefficient of thermal expansion, including:
[0022] The temperature difference at the core radius is determined based on the steady-state radial temperature distribution of the core, and multiple recursive constants are derived and calculated based on the temperature difference at the core radius, Young's modulus, Poisson's ratio and coefficient of thermal expansion.
[0023] The radial displacement of the cable core is calculated based on multiple recursive constants and the cable core radius.
[0024] Calculate the radial strain and circumferential strain based on the radial displacement and radius of the cable core, respectively;
[0025] The initial axial stress of the cable core is determined based on the temperature difference at the core radius, Young's modulus, Poisson's ratio, coefficient of thermal expansion, and multiple recursive constants.
[0026] Based on the initial axial stress of the cable core, the axial strain is determined using the stress equilibrium condition.
[0027] This embodiment provides a method for calculating the thermal stress and thermal strain of CORC cables. By establishing recursive expressions through stress-strain relationships, strain-displacement relationships, and continuity relationships, it achieves accurate calculation of the axial strain, radial strain, and circumferential strain of CORC cables. This lays the foundation for subsequent calculations of the thermal stress and thermal strain of CORC cables, avoiding the complex modeling and analysis steps and time-consuming calculation process of numerical simulation methods. It provides a convenient and effective means for assessing the low-temperature shrinkage of superconducting cables and designing related compensation engineering.
[0028] In one optional implementation, the temperature difference at the cable core radius is determined based on the steady-state radial temperature distribution of the cable core, and multiple recursive constants are derived and calculated based on the temperature difference at the cable core radius, Young's modulus, Poisson's ratio, and coefficient of thermal expansion, including:
[0029] Based on the temperature difference, Young's modulus, Poisson's ratio and coefficient of thermal expansion at the core radius, the radial continuity relationship between displacement and stress at the interface of the functional layers of the core is used to determine the pressure recursion constant.
[0030] Obtain the inner and outer surface pressures of the cable core, and calculate the contact pressure at the interface of the functional layers of the cable core based on the inner and outer surface pressures of the cable core and the pressure recursion constant.
[0031] The displacement recursive constant is determined based on the contact pressure at the interface of the functional layers of the cable core.
[0032] This embodiment provides a method for calculating the thermal stress and thermal strain of CORC cables. It utilizes the radial continuity relationship between displacement and stress at the interface of the functional layers of the cable core to determine the pressure recursive constant, and then calculates the contact pressure at the interface of the functional layers of the cable core. Based on the contact pressure at the interface of the functional layers of the cable core, it determines the displacement recursive constant, realizing the derivation and calculation of multiple recursive constants, and laying the foundation for subsequent derivation and calculation of the thermal stress and thermal strain of CORC cables.
[0033] In one optional implementation, the thermal stress of the CORC cable is calculated using the stress-strain relationship based on the thermal strain of the CORC cable, including:
[0034] The thermal stress of CORC cables is calculated based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, coefficient of thermal expansion, radial strain, circumferential strain, and axial strain of the cable core. The formula for calculating the thermal stress of CORC cables is as follows:
[0035] in, Indicates radial stress. Indicates circumferential stress. Indicates axial stress. Indicates radial strain. Indicates circumferential strain. E represents axial strain. i v represents the Young's modulus of the i-th functional layer of the cable core. i α represents the Poisson's ratio of the i-th functional layer of the cable core. i ΔT represents the coefficient of thermal expansion of the i-th functional layer of the cable core. i (r) represents the temperature difference at the radius r of the cable core.
[0036] Secondly, this application provides a device for calculating the thermal stress and thermal strain of CORC cables, the device comprising:
[0037] The first determining module is used to obtain the inner surface temperature and outer surface temperature of the core of the CORC cable, and to determine the steady-state radial temperature distribution of the core based on the inner surface temperature and outer surface temperature of the core using the heat balance equation of the CORC cable.
[0038] The second determining module is used to obtain the Young's modulus, Poisson's ratio, and coefficient of thermal expansion of the core functional layer. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, and coefficient of thermal expansion, the thermal strain of the CORC cable is determined using the stress-strain balance equation of the CORC cable. The thermal strain of the CORC cable includes radial strain, circumferential strain, and axial strain.
[0039] The calculation module is used to calculate the thermal stress of CORC cables based on their thermal strain and stress-strain relationship; the thermal stress of CORC cables includes radial stress, circumferential stress and axial stress.
[0040] Thirdly, this application provides a computer device, including: a memory and a processor, which are communicatively connected to each other. The memory stores computer instructions, and the processor executes the computer instructions to perform the method for calculating the thermal stress and thermal strain of the CORC cable described in the first aspect or any corresponding embodiment.
[0041] Fourthly, this application provides a computer-readable storage medium storing computer instructions for causing a computer to execute a method for calculating the thermal stress and thermal strain of a CORC cable according to the first aspect or any corresponding embodiment described above.
[0042] Fifthly, this application provides a computer program product, including computer instructions for causing a computer to execute a method for calculating the thermal stress and thermal strain of a CORC cable according to the first aspect or any corresponding embodiment described above. Attached Figure Description
[0043] To more clearly illustrate the technical solutions in the specific embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0044] Figure 1 is a flowchart illustrating a method for calculating the thermal stress and thermal strain of a CORC cable according to an embodiment of this application.
[0045] Figure 2 is a flowchart illustrating another method for calculating the thermal stress and thermal strain of a CORC cable according to an embodiment of this application.
[0046] Figure 3 is a schematic diagram of a composite CORC cable core structure according to an embodiment of this application;
[0047] Figure 4 is a flowchart illustrating another method for calculating the thermal stress and thermal strain of a CORC cable according to an embodiment of this application.
[0048] Figure 5 is a schematic diagram of stress components in cylindrical coordinates according to an embodiment of this application;
[0049] Figure 6 is a flowchart illustrating the calculation method for thermal stress and thermal strain of CORC cable based on the recursive method according to an embodiment of this application.
[0050] Figure 7 is a comparison of the radial and circumferential thermal strain obtained by numerical simulation according to the embodiments of this application with the calculation results of the recursive method;
[0051] Figure 8 is a comparison diagram of thermal stress in each direction obtained by numerical simulation according to the embodiments of this application and the calculation results of the recursive method;
[0052] Figure 9 is a structural block diagram of a CORC cable thermal stress and thermal strain calculation device according to an embodiment of this application;
[0053] Figure 10 is a schematic diagram of the hardware structure of a computer device according to an embodiment of this application. Detailed Implementation
[0054] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0055] The method for assessing the shrinkage of superconducting cables at low temperatures generally employs an empirical formula method. This method uses the outer Dewar tube of the superconducting cable as a reference, taking the coefficient of thermal expansion as the material parameters of a double-layer stainless steel corrugated tube, with a shrinkage range of approximately 3‰. However, as a composite structure, the superconducting cable core has different geometric and material parameters for each conductor layer and functional layer. The empirical formula method, using stainless steel as a reference, is inaccurate in calculating deformation and cannot calculate stress.
[0056] In addition, numerical simulation methods are used, specifically in finite element simulation software, to calculate the thermal stress and thermal strain of the composite CORC cable in superconducting cables during thermal cycles using thermal expansion boundary conditions. However, numerical simulation methods also have limitations: firstly, they require the establishment of complex numerical models, including geometry, materials, physical fields and boundary conditions, mesh and solver settings; secondly, numerical models typically have long computation times, especially for helical three-dimensional CORC cable models, where the large number of meshes places high demands on computer simulation hardware, and the non-Cartesian coordinate system makes post-processing more complicated.
[0057] To address the aforementioned technical problems, this application provides a method for calculating the thermal stress and thermal strain of CORC cables. The calculation is divided into two parts: thermal and mechanical. In the thermal part, the radial temperature distribution of the CORC cable in steady state is calculated using the thermal balance equation, Fourier's law, and temperature / heat transfer boundary conditions. In the mechanical part, recursive expressions are established using stress-strain relationships, strain-displacement relationships, and continuity relationships. Then, the CORC cable temperature is substituted into the stress-strain expressions of each functional layer to obtain the thermal stress and thermal strain of the CORC cable at the current temperature. This method reasonably considers the thermal stress and thermal strain during the low-temperature shrinkage process of the CORC cable. The calculation principle is clear, the calculation process is simple and easy to operate, and the calculation results are relatively accurate. It avoids the complex modeling and analysis steps and time-consuming calculation process of numerical simulation methods. It can reasonably reflect the degree of low-temperature shrinkage of CORC cables and has a simplified solution process, providing a portable and effective method for compensating for the low-temperature shrinkage of CORC cables, taking into account both technical significance and engineering practical value.
[0058] This application provides a method for calculating the thermal stress and thermal strain of CORC cables. It should be noted that the execution subject of this method can be a CORC cable thermal stress and thermal strain calculation device. This device can be implemented as part or all of an electronic device through software, hardware, or a combination of both. The electronic device can be a server or a terminal. In this application embodiment, the server can be a single server or a server cluster composed of multiple servers. The terminal can be a smartphone, personal computer, tablet computer, wearable device, or other intelligent hardware device such as a smart robot. The following method embodiments all use an electronic device as the execution subject for illustration.
[0059] According to an embodiment of this application, a method for calculating the thermal stress and thermal strain of a CORC cable is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.
[0060] This embodiment provides a method for calculating the thermal stress and thermal strain of a CORC cable, which can be used in the aforementioned electronic equipment. Figure 1 is a flowchart of a method for calculating the thermal stress and thermal strain of a CORC cable according to an embodiment of this application. As shown in Figure 1, the process includes the following steps:
[0061] Step S101: Obtain the inner surface temperature and outer surface temperature of the CORC cable core. Based on the inner surface temperature and outer surface temperature of the cable core, determine the steady-state radial temperature distribution of the cable core using the CORC cable heat balance equation.
[0062] Specifically, since both ends of the CORC cable are connected to the superconducting cable terminal, the displacement of each functional layer in the cable core axis is the same. Under the support of the stainless steel corrugated tube skeleton and the tight winding of the protective layer, the interfaces between the functional layers can be regarded as completely bonded. Therefore, ignoring the influence of air gaps between the superconducting tapes of the conductor layer and the semi-overlapping process, the spirally wound CORC cable core can be simplified into an axisymmetric composite structure.
[0063] Step S102: Obtain the Young's modulus, Poisson's ratio, and coefficient of thermal expansion of the functional layer of the cable core. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, and coefficient of thermal expansion, determine the thermal strain of the CORC cable using the stress-strain balance equation of the CORC cable. The thermal strain of the CORC cable includes radial strain, circumferential strain, and axial strain.
[0064] Step S103: Based on the thermal strain of the CORC cable, calculate the thermal stress of the CORC cable using the stress-strain relationship; the thermal stress of the CORC cable includes radial stress, circumferential stress and axial stress.
[0065] This embodiment provides a method for calculating the thermal stress and thermal strain of CORC cables. Based on the inner and outer surface temperatures of the cable core, the steady-state radial temperature distribution of the cable core is determined using the thermal balance equation of the CORC cable. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, and coefficient of thermal expansion, the thermal strain of the CORC cable is determined using the stress-strain balance equation of the CORC cable. Based on the thermal strain of the CORC cable, the thermal stress of the CORC cable is calculated using the stress-strain relationship. This method achieves a reasonable analysis of the thermal stress and thermal strain of CORC cables, avoiding the complex modeling and analysis steps and time-consuming calculation process of numerical simulation methods. It can reasonably reflect the degree of low-temperature shrinkage of CORC cables and has a simplified solution process, providing a portable and effective method for compensating for low-temperature shrinkage of CORC cables, taking into account both technical significance and engineering practical value.
[0066] This embodiment provides a method for calculating the thermal stress and thermal strain of a CORC cable, which can be used in the aforementioned electronic equipment. Figure 2 is a flowchart of a method for calculating the thermal stress and thermal strain of a CORC cable according to an embodiment of this application. As shown in Figure 2, the process includes the following steps:
[0067] Step S201: Obtain the inner surface temperature and outer surface temperature of the CORC cable core. Based on the inner surface temperature and outer surface temperature of the cable core, determine the steady-state radial temperature distribution of the cable core using the CORC cable heat balance equation.
[0068] Specifically, step S201 includes:
[0069] Step S2011: Obtain the inner surface temperature and outer surface temperature of the CORC cable core, and calculate the heat flux at the core radius based on the inner surface temperature and outer surface temperature of the core.
[0070] Specifically, when the temperatures of the inner and outer surfaces of the cable core are obtained (temperatures are measured inside and outside the cable), the heat flux at the radius of the cable core under the Dirichlet boundary condition is calculated; when the physical properties of the cable core material and the refrigerant (liquid nitrogen) are obtained, the heat flux at the radius of the cable core under the mixed boundary condition is calculated; different boundary conditions can be selected according to the situation.
[0071] In some optional implementations, step S2011 above includes:
[0072] Step a1: Obtain the surface parameters of the cable core functional layer, and calculate the heat flux at the cable core radius under the Dirichlet boundary conditions based on the inner surface temperature of the cable core, the outer surface temperature of the cable core, and the surface parameters of the cable core functional layer.
[0073] Specifically, the composite CORC cable core structure is shown in Figure 3. From the inner layer to the outer layer, the surface parameters of the cable core functional layers include: the radius, temperature, and thermal conductivity of each cable core functional layer surface are r, respectively. i T i and k i ,i=0,1,2,…,N;T i h is the temperature of the inner surface of the cable core. i p0 is the convective heat transfer coefficient of the inner surface of the cable core; T is the pressure on the inner surface of the cable core. o h is the temperature of the outer surface of the cable core. o p is the convective heat transfer coefficient of the cable core outer surface; N This refers to the pressure on the outer surface of the cable core.
[0074] Alternatively, in cylindrical coordinates, the general form of the heat conduction equation is:
[0075] Where f is the heat source, i is the number of functional layers in the cable core, i = 1, 2, ..., N, r, θ and z are the radial, circumferential and axial coordinates respectively, and ρ i Let c be the density of the i-th functional layer. i Let be the specific heat capacity of the i-th functional layer, and t be the time operator.
[0076] Optionally, for superconducting cables, the heat sources in the cable core consist only of the AC losses of the conductor layer and the viscous losses of the convective heat transfer surface, which can be neglected. Therefore, the heat conduction equation of the i-th layer in steady state can be simplified to:
[0077] Alternatively, the heat flux q(r) at the cable core radius r can be calculated using Fourier's law according to the above formula (2):
[0078] Optionally, when the temperatures of the inner and outer surfaces of the cable core are constant, or when the convective heat transfer coefficients between the inner and outer surfaces of the cable core and liquid nitrogen tend to infinity, the heat flux of the CORC cable core at the cable core radius r under the Dirichlet boundary conditions is:
[0079] Step a2, or, obtain the heat transfer coefficient of the inner surface of the cable core and the heat transfer coefficient of the outer surface of the cable core, and calculate the heat flux at the radius of the cable core under mixed boundary conditions based on the inner surface temperature of the cable core, the outer surface temperature of the cable core, the surface parameters of the functional layer of the cable core, the heat transfer coefficient of the inner surface of the cable core, and the heat transfer coefficient of the outer surface of the cable core.
[0080] Specifically, for mixed boundary conditions, the heat transfer coefficient h on the inner surface of the cable core is used. i and the heat transfer coefficient h of the outer surface of the cable core o The heat flux q(r) at the cable core radius r is calculated using the following formula:
[0081] Step S2012: Determine the steady-state radial temperature distribution based on the heat flux at the cable core radius.
[0082] Specifically, based on the heat flux q(r) at the core radius r, without considering heat accumulation or dissipation, the steady-state radial temperature distribution of the core is obtained by integrating along the core radius r. The steady-state radial temperature distribution of the core can be expressed as:
[0083] Step S202: Obtain the Young's modulus, Poisson's ratio, and coefficient of thermal expansion of the functional layer of the cable core. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, and coefficient of thermal expansion, determine the thermal strain of the CORC cable using the stress-strain balance equation of the CORC cable. The thermal strain of the CORC cable includes radial strain, circumferential strain, and axial strain. For details, please refer to step S102 of the embodiment shown in Figure 1, which will not be repeated here.
[0084] Step S203: Based on the thermal strain of the CORC cable, calculate the thermal stress of the CORC cable using the stress-strain relationship; the thermal stress of the CORC cable includes radial stress, circumferential stress, and axial stress. For details, please refer to step S103 of the embodiment shown in Figure 1, which will not be repeated here.
[0085] This embodiment provides a method for calculating the thermal stress and thermal strain of CORC cables. It calculates the heat flux at the cable core radius using the inner and outer surface temperatures of the cable core, thereby determining the steady-state radial temperature distribution. The method derives the function of temperature versus radius using the CORC cable's thermal balance equation, neglecting the effects of air gaps between superconducting tapes, semi-overlapping processes, AC losses in the conductor layer, and viscous losses in the convective heat transfer surface. This method reasonably reflects the structural characteristics and application conditions of CORC cables and is easily solvable, providing a scientific basis and effective means for assessing the low-temperature shrinkage of superconducting cables.
[0086] This embodiment provides a method for calculating the thermal stress and thermal strain of a CORC cable, which can be used in the aforementioned electronic equipment. Figure 4 is a flowchart of a method for calculating the thermal stress and thermal strain of a CORC cable according to an embodiment of this application. As shown in Figure 4, the process includes the following steps:
[0087] Step S401: Obtain the inner surface temperature and outer surface temperature of the CORC cable core. Based on these temperatures, determine the steady-state radial temperature distribution of the cable core using the CORC cable's heat balance equation. For details, please refer to step S201 of the embodiment shown in Figure 2, which will not be repeated here.
[0088] Step S402: Obtain the Young's modulus, Poisson's ratio, and coefficient of thermal expansion of the functional layer of the cable core. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, and coefficient of thermal expansion, determine the thermal strain of the CORC cable using the stress-strain balance equation of the CORC cable. The thermal strain of the CORC cable includes radial strain, circumferential strain, and axial strain.
[0089] Specifically, as shown in Figure 5, for the axial shrinkage of the cable at low temperatures, the dependent variable is the axial strain ε. zz However, the recursive method for calculating the stress and strain of the cable core requires that there are no variables in the calculation steps. Therefore, we first assume that the axial strain of the cable core is 0.
[0090] Step S402 above includes:
[0091] Step S4021: Determine the temperature difference at the radius of the cable core based on the steady-state radial temperature distribution of the cable core, and derive and calculate multiple recursive constants based on the temperature difference at the radius of the cable core, Young's modulus, Poisson's ratio and coefficient of thermal expansion.
[0092] Specifically, the temperature difference at the core radius is the temperature T at the core radius r. i (r) and initial reference temperature T ref The difference.
[0093] Alternatively, assuming complete bonding between the interfaces of the cable core functional layers, the recursive constant δ in the pressure expression is determined by the radial continuity relationship between displacement and stress at the interfaces of the cable core functional layers. i+1 C i D i and F i Then, based on the constants G0, G1, H0, and H1, the recursive constant G in the pressure expression is determined. i and H i .
[0094] In some optional implementations, step S4021 above includes:
[0095] Step b1: Based on the temperature difference, Young's modulus, Poisson's ratio, and coefficient of thermal expansion at the core radius, the radial continuity relationship between displacement and stress at the interface of the functional layers of the core is used to determine the pressure recursion constant.
[0096] Specifically, the stress-strain relationship of the i-th anisotropic material is as follows:
[0097] Where, ΔT i (r) represents the temperature difference at the cable core radius r, and its value is equal to the temperature T at the cable core radius r. i (r) and initial reference temperature T ref The difference, E i v represents the Young's modulus of the i-th functional layer of the cable core. i α represents the Poisson's ratio of the i-th functional layer of the cable core. i The coefficient of thermal expansion of the i-th cable core functional layer is represented by σ and ε, respectively, and the subscripts rr, θθ and zz represent radial, circumferential and axial directions, respectively. The superscript i represents the i-th cable core functional layer.
[0098] Optionally, under axisymmetric loading, the stress and strain of the cable core are independent of the circumferential coordinate θ, while the radial and axial displacements depend only on their respective coordinates. Therefore, the strain-displacement relationship simplified from the i-th layer of the cable core in cylindrical coordinates can be expressed as:
[0099] in, This represents the radial displacement of the i-th cable core functional layer.
[0100] Alternatively, since the stress in the cable core is independent of the axial coordinate z, the equilibrium equations for the radial and circumferential stresses in the i-th layer of the cable core are:
[0101] Optionally, substituting equation (8) into equation (7) and then into equation (9) yields the stress equilibrium equation expressed in terms of displacement:
[0102] Alternatively, integrating the above formula along the cable core radius r, the radial displacement of the cable core is:
[0103] Among them, the intermediate parameter I corresponding to the i-th layer of the cable core functional layer i (r), β i and γ i It can be represented as:
[0104] Alternatively, assuming complete bonding between functional layer interfaces, the radial displacement and radial stress at the interfaces of each cable core functional layer are continuous. Therefore, the radial continuity relationship at the interfaces of the cable core functional layers is as follows:
[0105] Optionally, according to I in the above formula (12) i The definition of (r), I i+1 (r iThe value of ) is 0, therefore, the displacement recursion constant A in the expression for the radial displacement of the cable core is 0. i+1 and B i+1 for:
[0106] Optionally, in order to determine the constant A in the above equation i+1 and B i+1 The radial stress at the interface of the functional layers of the cable core, expressed as contact pressure, is:
[0107] Among them, according to the above formula (15), the pressure recursion constant δ i+1 C i D i and F i It can be represented as:
[0108] Optionally, based on the radial stress at the interface of the functional layers of the cable core, expressed as contact pressure, the contact pressure on the outer surface of the i-th layer of the cable core is:
[0109] Optionally, the displacement recursion constant A in the above formula (15) can be... i and B i Substituting into the above formula (17), the contact pressure at the interface of the cable core functional layers is:
[0110] Alternatively, simplifying the above formula (18), the contact pressure at the interface of the cable core functional layers can be expressed by the following formula: p i+1 =G i+1 p1+H i+1 p0 (19)
[0111] Where p0 is the pressure on the inner surface of the cable core, and the pressure recursion constant G i+1 and H i+1 It can be represented as:
[0112] In the above formula, G0 = 0, G1 = 1, H0 = 1, and H1 = 0.
[0113] Step b2: Obtain the inner surface pressure and outer surface pressure of the cable core, and calculate the contact pressure at the interface of the functional layers of the cable core based on the inner surface pressure, outer surface pressure and pressure recursion constant.
[0114] Specifically, through the inner surface pressure p0 and the outer surface pressure p of the cable core N The contact pressure at each interface of the cable core is calculated using the general formula of the pressure expression. That is, when i = N-1, the formula for calculating the contact pressure p1 at the interface of the functional layers of the cable core is:
[0115] In the formula, p N This refers to the pressure on the outer surface of the cable core.
[0116] Optionally, due to the pressure p0 on the inner surface of the cable core and the pressure p on the outer surface, the engineering cable core... N Both can be measured using a cable cryogenic system; therefore, the contact pressure p at the interface of the functional layers of the cable core is... i It can be determined by the following recursive relation:
[0117] Step b3: Determine the displacement recursive constant based on the contact pressure at the interface of the cable core functional layers.
[0118] Specifically, the contact pressure p at the interface of the aforementioned cable core functional layers i Substituting into the above formula (15), we obtain the displacement recursive constant, the displacement recursive constant A. i and B i It can be represented as:
[0119] Step S4022: Calculate the radial displacement of the cable core based on multiple recursive constants and the cable core radius.
[0120] Specifically, by using the displacement recursion constant A i and B i The formula for calculating the radial displacement of the cable core at radius r is as follows:
[0121] Step S4023: Calculate the radial strain and circumferential strain based on the cable core radial displacement and cable core radius, respectively.
[0122] Specifically, the radial strain of the cable core is calculated using the strain-displacement relationship in formula (8) above. and circumferential strain
[0123] Step S4024: Determine the initial axial stress of the cable core based on the temperature difference at the core radius, Young's modulus, Poisson's ratio, coefficient of thermal expansion, and multiple recursive constants.
[0124] Specifically, assuming the axial strain of the cable core is 0, the formula for calculating the initial axial stress of the cable core is as follows:
[0125] Step S4025: Based on the initial axial stress of the cable core, determine the axial strain using the stress balance condition.
[0126] Specifically, considering the axial shrinkage of the cable under thermal-mechanical load, the axial external load F is applied. zTo calculate the axial strain of the cable core, based on the stress equilibrium condition (i.e., the resultant axial force at the cable end face equals the external load), the actual axial strain of the cable core is:
[0127] Step S403: Based on the thermal strain of the CORC cable, calculate the thermal stress of the CORC cable using the stress-strain relationship; the thermal stress of the CORC cable includes radial stress, circumferential stress and axial stress.
[0128] Specifically, the thermal stress of the CORC cable is calculated based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, coefficient of thermal expansion, radial strain, circumferential strain, and axial strain of the cable core.
[0129] Alternatively, based on fundamental engineering mechanics, the mechanical behavior of a cable from axial strain of 0 to response to an axial external load, without loads in other directions, is uniaxial tension. Therefore, the axial and circumferential strains of the cable core remain unchanged. According to the stress-strain relationship, the actual stress of the cable core under thermo-mechanical load is:
[0130] in, Indicates radial stress. Indicates circumferential stress. Indicates axial stress. Indicates radial strain. Indicates circumferential strain. E represents axial strain. i v represents the Young's modulus of the i-th functional layer of the cable core. i α represents the Poisson's ratio of the i-th functional layer of the cable core. i ΔT represents the coefficient of thermal expansion of the i-th functional layer of the cable core. i (r) represents the temperature difference at the radius r of the cable core.
[0131] This embodiment provides a method for calculating the thermal stress and thermal strain of CORC cables. By establishing recursive expressions through stress-strain relationships, strain-displacement relationships, and continuity relationships, it achieves accurate calculation of the axial strain, radial strain, and circumferential strain of CORC cables. This lays the foundation for subsequent calculations of the thermal stress and thermal strain of CORC cables, avoiding the complex modeling and analysis steps and time-consuming calculation process of numerical simulation methods. It provides a convenient and effective means for assessing the low-temperature shrinkage of superconducting cables and designing related compensation engineering.
[0132] The following specific embodiment illustrates the steps and beneficial effects of a method for calculating the thermal stress and thermal strain of a CORC cable.
[0133] Example 1:
[0134] As shown in Figure 6, the steps for calculating the thermal stress and thermal strain of CORC cables include:
[0135] Step 1001: For the Dirichlet boundary condition, the temperature T on the inner surface of the cable core is used as the reference. i and external surface temperature T o Calculate the heat flux at the cable core radius r;
[0136] Step 1002: For mixed boundary conditions, the heat transfer coefficient h of the inner surface of the cable core is used. i and the heat transfer coefficient h of the outer surface o Calculate the heat flux at the cable core radius r;
[0137] Step 1003: Based on the calculated heat flux q(r), without considering heat accumulation or dissipation, integrate along the core radius r to obtain the steady-state radial temperature distribution of the core.
[0138] Step 1004: Assuming complete bonding between the interfaces of the cable core functional layers, determine the pressure recursion constant δ in the pressure expression based on the radial continuity relationship between displacement and stress at the interface of the cable core functional layers. i+1 C i D i and F i ;
[0139] Step 1005: Based on constants G0, G1, H0, and H1, determine the pressure recursion constant G in the general formula of the pressure expression. i and H i ;
[0140] Step 1006: By controlling the pressure p0 on the inner surface of the cable core and the pressure p on the outer surface... N The contact pressure at the interface of the functional layers of the cable core is calculated using the general formula of the pressure expression.
[0141] Step 1007: Determine the displacement recursion constant A in the radial displacement expression. i and B i ;
[0142] Step 1008: Deducing the constant A from the displacement recurrence relation i and B i Calculate the radial displacement at the cable core radius r;
[0143] Step 1009: Optionally, calculate the radial strain and circumferential strain of the cable core using the strain-displacement relationship;
[0144] Step 1010: Calculate the axial stress of the cable core based on the assumption that the axial strain of the cable core is 0;
[0145] Step 1011: Considering the axial shrinkage of the cable under thermal-mechanical load, apply an axial external load Fz Calculate the axial strain of the cable core;
[0146] Step 1012: Finally, using the calculated axial strain, the true radial stress, circumferential stress, and axial stress of the cable core are calculated from the stress-strain relationship.
[0147] Example 2:
[0148] Select the geometric and material parameters of a certain composite structure, including: inner diameter r i-1 Outer diameter r i Young's modulus E i Poisson's ratio v i Coefficient of thermal expansion α i and thermal conductivity k i Assuming the temperature difference between the inner and outer surfaces is 70K, and the pressures on the inner and outer surfaces are 22MPa and 1.5MPa respectively, the geometric and material parameter settings are shown in Table 1 below:
[0149] Table 1:
[0150] The above example was numerically simulated and analyzed using the commercial software COMSOL Multiphysics, and thermal stress and thermal strain were calculated through thermal expansion.
[0151] Figure 7 is a comparison of the radial thermal strain and circumferential thermal strain at various points in the radial direction obtained from the numerical simulation with the calculated results of the thermal stress and strain of the CORC cable based on the recursive method. Figure 8 is a comparison of the thermal stress at various points in the radial direction obtained from the numerical simulation with the calculated results of the thermal stress and strain of the CORC cable based on the recursive method. As shown in Figures 7 and 8, the distribution curves of the two are quite similar and have basically consistent variation characteristics.
[0152] Furthermore, the maximum relative error between numerical simulation and the recursive method for calculating the thermal stress and strain of CORC cables is 0.55% for radial displacement and 0.6% for circumferential strain. It should be noted that the recursive method for calculating the thermal stress and strain of CORC cables first assumes an initial axial strain of 0, describing the material's mechanical behavior under external load using uniaxial tension. That is, it calculates the true axial strain of the composite model based on stress equilibrium conditions, neglecting the effect of axial stress on radial and circumferential strain. This is one of the main reasons for the discrepancy between the numerical simulation results and the actual calculations.
[0153] In the above embodiments, the calculation of thermal stress and strain of CORC cables is based on clear thermodynamic concepts and rigorous derivations. The function of temperature versus radius is derived from the thermal balance equation of the CORC cable, and the recursive equations for interface pressure, radial displacement, strain, and stress are derived from the stress-strain balance equation of the CORC cable, thus determining the thermal stress and strain of the CORC cable at the current temperature. Simultaneously, the effects of air gaps between superconducting tapes, semi-overlapping processes, AC losses in the conductor layer, and viscous losses in the convective heat transfer surface are ignored. This approach reasonably reflects the structural characteristics and application conditions of CORC cables and is easily solvable, providing a scientific basis and effective means for assessing the low-temperature shrinkage of superconducting cables. Finally, the thermal stress and strain of the CORC cable are calculated quickly using a simple calculation program. The calculation process is simple, time-efficient, and yields relatively accurate results, avoiding the complex modeling and analysis steps and time-consuming calculations of numerical simulation methods. This provides a convenient and effective means for assessing the low-temperature shrinkage of superconducting cables and designing related compensation engineering.
[0154] This embodiment also provides a device for calculating the thermal stress and thermal strain of CORC cables. This device is used to implement the above embodiments and optional implementation methods, and details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.
[0155] This embodiment provides a device for calculating the thermal stress and thermal strain of CORC cables, as shown in Figure 9, including:
[0156] The first determining module 901 is used to obtain the inner surface temperature and outer surface temperature of the core of the CORC cable, and to determine the steady-state radial temperature distribution of the core based on the inner surface temperature and outer surface temperature of the core using the heat balance equation of the CORC cable.
[0157] The second determining module 902 is used to obtain the Young's modulus, Poisson's ratio and coefficient of thermal expansion of the core functional layer. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio and coefficient of thermal expansion, the thermal strain of the CORC cable is determined using the stress-strain balance equation of the CORC cable. The thermal strain of the CORC cable includes radial strain, circumferential strain and axial strain.
[0158] The calculation module 903 is used to calculate the thermal stress of the CORC cable based on the thermal strain of the CORC cable and using the stress-strain relationship; the thermal stress of the CORC cable includes radial stress, circumferential stress and axial stress.
[0159] In some alternative implementations, the first determining module 901 includes:
[0160] The first calculation unit is used to obtain the inner surface temperature and outer surface temperature of the core of the CORC cable, and calculate the heat flux at the core radius based on the inner surface temperature and outer surface temperature of the core.
[0161] The first determining unit is used to determine the steady-state radial temperature distribution based on the heat flux at the cable core radius.
[0162] In some alternative implementations, the first computing unit includes:
[0163] The first calculation subunit is used to obtain the surface parameters of the cable core functional layer and calculate the heat flux at the cable core radius under the Dirichlet boundary conditions based on the cable core inner surface temperature, cable core outer surface temperature and cable core functional layer surface parameters.
[0164] The second calculation subunit is used to obtain the heat transfer coefficient of the inner surface and the heat transfer coefficient of the outer surface of the cable core, and to calculate the heat flux at the radius of the cable core under mixed boundary conditions based on the inner surface temperature, outer surface temperature, surface parameters of the functional layer of the cable core, and the heat transfer coefficient of the inner and outer surfaces of the cable core.
[0165] In some alternative implementations, the second determining module 902 includes:
[0166] The second calculation unit is used to determine the temperature difference at the radius of the cable core based on the steady-state radial temperature distribution of the cable core, and to derive and calculate multiple recursive constants based on the temperature difference at the radius of the cable core, Young's modulus, Poisson's ratio and coefficient of thermal expansion.
[0167] The third calculation unit is used to calculate the radial displacement of the cable core based on multiple recursive constants and the cable core radius;
[0168] The fourth calculation unit is used to calculate the radial strain and circumferential strain based on the radial displacement and radius of the cable core, respectively.
[0169] The second determining unit is used to determine the initial axial stress of the cable core based on the temperature difference at the cable core radius, Young's modulus, Poisson's ratio, coefficient of thermal expansion and multiple recursive constants.
[0170] The third determining unit is used to determine the axial strain based on the initial axial stress of the cable core and the stress balance condition.
[0171] In some alternative implementations, the second computing unit includes:
[0172] The first determining subunit is used to determine the pressure recursive constant based on the temperature difference, Young's modulus, Poisson's ratio and thermal expansion coefficient at the core radius, using the radial continuity relationship between displacement and stress at the interface of the functional layers of the core.
[0173] The third calculation subunit is used to obtain the inner surface pressure and outer surface pressure of the cable core, and calculate the contact pressure at the interface of the functional layers of the cable core based on the inner surface pressure, outer surface pressure and pressure recursion constant.
[0174] The second determining sub-unit is used to determine the displacement recursive constant based on the contact pressure at the interface of the cable core functional layers.
[0175] In some optional implementations, the calculation module 903 is specifically used to calculate the thermal stress of the CORC cable based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, coefficient of thermal expansion, radial strain, circumferential strain, and axial strain of the cable core. The formula for calculating the thermal stress of the CORC cable is as follows:
[0176] in, Indicates radial stress. Indicates circumferential stress. Indicates axial stress. Indicates radial strain. Indicates circumferential strain. E represents axial strain. i v represents the Young's modulus of the i-th functional layer of the cable core. i α represents the Poisson's ratio of the i-th functional layer of the cable core. i ΔT represents the coefficient of thermal expansion of the i-th functional layer of the cable core. i (r) represents the temperature difference at the radius r of the cable core.
[0177] The optional functional descriptions of the above modules and units are the same as those in the corresponding embodiments described above, and will not be repeated here.
[0178] In this embodiment, the device for calculating the thermal stress and thermal strain of a CORC cable is presented in the form of a functional unit. Here, a unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and memory that execute one or more software or fixed programs, and / or other devices that can provide the above functions.
[0179] This application also provides a computer device having a calculation apparatus for the thermal stress and thermal strain of a CORC cable as shown in FIG9 above.
[0180] Please refer to Figure 10, which is a schematic diagram of the structure of a computer device provided in an optional embodiment of this application. As shown in Figure 10, the computer device includes: one or more processors 10, memory 20, and interfaces for connecting the various components, including high-speed interfaces and low-speed interfaces. The various components communicate with each other using different buses and can be installed on a common motherboard or otherwise as needed. The processor can process instructions executed within the computer device, including instructions stored in or on memory to display graphical information of a GUI on an external input / output device (such as a display device coupled to the interface). In some optional embodiments, multiple processors and / or multiple buses can be used with multiple memories, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 10 shows an example of a single processor 10.
[0181] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Optionally, processor 10 may also include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The programmable logic device may be a complex programmable logic device (CLP), a field-programmable gate array (FPGA), a general-purpose array logic (GPRS), or any combination thereof.
[0182] The memory 20 stores instructions executable by at least one processor 10 to cause the at least one processor 10 to perform the method shown in the above embodiments.
[0183] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.
[0184] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.
[0185] The computer device also includes a communication interface 30 for communicating with other devices or communication networks.
[0186] This application also provides a computer-readable storage medium. The methods described in this application can be implemented in hardware or firmware, or implemented as recordable on a storage medium, or implemented as computer code downloaded over a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and subsequently stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; optionally, the storage medium may also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods shown in the above embodiments.
[0187] A portion of this application can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to this application through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.
[0188] Although embodiments of this application have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of this application, and all such modifications and variations fall within the scope defined by the appended claims.
Claims
1. A method for calculating the thermal stress and thermal strain of a CORC cable, characterized in that, The method includes: The inner surface temperature and outer surface temperature of the core of the CORC cable are obtained. Based on the inner surface temperature and outer surface temperature of the core, the steady-state radial temperature distribution of the core is determined using the heat balance equation of the CORC cable. The Young's modulus, Poisson's ratio, and coefficient of thermal expansion of the core functional layer are obtained. Based on the steady-state radial temperature distribution, the Young's modulus, the Poisson's ratio, and the coefficient of thermal expansion, the thermal strain of the CORC cable is determined using the stress-strain balance equation of the CORC cable. The thermal strain of the CORC cable includes radial strain, circumferential strain, and axial strain. Based on the thermal strain of the CORC cable, the thermal stress of the CORC cable is calculated using the stress-strain relationship; the thermal stress of the CORC cable includes radial stress, circumferential stress, and axial stress.
2. The method according to claim 1, characterized in that, The determination of the steady-state radial temperature distribution of the cable core based on the inner and outer surface temperatures of the cable core, using the CORC cable thermal balance equation, includes: Obtain the inner surface temperature and outer surface temperature of the CORC cable core, and calculate the heat flux at the core radius based on the inner surface temperature and outer surface temperature of the core. The steady-state radial temperature distribution is determined based on the heat flux at the radius of the cable core.
3. The method according to claim 2, characterized in that, The calculation of the heat flux at the radius of the cable core based on the inner surface temperature and the outer surface temperature of the cable core includes: Obtain the surface parameters of the cable core functional layer, and calculate the heat flux at the radius of the cable core under the Dirichlet boundary conditions based on the inner surface temperature of the cable core, the outer surface temperature of the cable core, and the surface parameters of the cable core functional layer. Alternatively, the heat transfer coefficients of the inner and outer surfaces of the cable core can be obtained, and the heat flux at the radius of the cable core under mixed boundary conditions can be calculated based on the inner surface temperature, the outer surface temperature, the surface parameters of the functional layer of the cable core, the heat transfer coefficients of the inner and outer surfaces of the cable core.
4. The method according to claim 1, characterized in that, The determination of the thermal strain of the CORC cable based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, and coefficient of thermal expansion using the stress-strain balance equation of the CORC cable includes: The temperature difference at the radius of the cable core is determined based on the steady-state radial temperature distribution of the cable core, and multiple recursive constants are derived and calculated based on the temperature difference at the radius of the cable core, the Young's modulus, the Poisson's ratio, and the coefficient of thermal expansion. The radial displacement of the cable core is calculated based on the multiple recursive constants and the cable core radius; The radial strain and the circumferential strain are calculated based on the radial displacement of the cable core and the radius of the cable core, respectively. The initial axial stress of the cable core is determined based on the temperature difference at the radius of the cable core, the Young's modulus, the Poisson's ratio, the coefficient of thermal expansion, and the plurality of recursive constants. The axial strain is determined based on the initial axial stress of the cable core using stress equilibrium conditions.
5. The method according to claim 4, characterized in that, The temperature difference at the cable core radius is determined based on the steady-state radial temperature distribution of the cable core, and multiple recursive constants are derived and calculated based on the temperature difference at the cable core radius, the Young's modulus, the Poisson's ratio, and the coefficient of thermal expansion, including: Based on the temperature difference at the core radius, the Young's modulus, the Poisson's ratio, and the coefficient of thermal expansion, the pressure recursion constant is determined by utilizing the radial continuity relationship between displacement and stress at the interface of the core functional layers. Obtain the inner surface pressure and outer surface pressure of the cable core, and calculate the contact pressure at the interface of the functional layers of the cable core based on the inner surface pressure, the outer surface pressure and the pressure recursion constant. The displacement recursive constant is determined based on the contact pressure at the interface of the functional layers of the cable core.
6. The method according to claim 1, characterized in that, The calculation of the thermal stress of the CORC cable based on its thermal strain and using the stress-strain relationship includes: The thermal stress of the CORC cable is calculated based on the steady-state radial temperature distribution of the cable core, the Young's modulus, the Poisson's ratio, the coefficient of thermal expansion, the radial strain, the circumferential strain, and the axial strain. The formula for calculating the thermal stress of the CORC cable is as follows: in, Indicates radial stress. Indicates circumferential stress. Indicates axial stress. Indicates radial strain. Indicates circumferential strain. E represents axial strain. i v represents the Young's modulus of the i-th functional layer of the cable core. i α represents the Poisson's ratio of the i-th functional layer of the cable core. i ΔT represents the coefficient of thermal expansion of the i-th functional layer of the cable core. i (r) represents the temperature difference at the radius r of the cable core.
7. A device for calculating the thermal stress and thermal strain of CORC cables, characterized in that, The device includes: The first determining module is used to obtain the inner surface temperature and outer surface temperature of the core of the CORC cable, and to determine the steady-state radial temperature distribution of the core based on the inner surface temperature and the outer surface temperature of the core using the heat balance equation of the CORC cable. The second determining module is used to obtain the Young's modulus, Poisson's ratio, and coefficient of thermal expansion of the core functional layer. Based on the steady-state radial temperature distribution, the Young's modulus, the Poisson's ratio, and the coefficient of thermal expansion, the thermal strain of the CORC cable is determined using the stress-strain balance equation of the CORC cable. The thermal strain of the CORC cable includes radial strain, circumferential strain, and axial strain. The calculation module is used to calculate the thermal stress of the CORC cable based on the thermal strain of the CORC cable using the stress-strain relationship; the thermal stress of the CORC cable includes radial stress, circumferential stress and axial stress.
8. A computer device, characterized in that, include: A memory and a processor are interconnected, the memory stores computer instructions, and the processor executes the computer instructions to perform the calculation method for thermal stress and thermal strain of the CORC cable as described in any one of claims 1 to 6.
9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a computer to execute the calculation method for the thermal stress and thermal strain of the CORC cable according to any one of claims 1 to 6.
10. A computer program product, characterized in that, Includes computer instructions for causing a computer to execute a method for calculating the thermal stress and thermal strain of the CORC cable as described in any one of claims 1 to 6.