Method and device for calculating thermal stress and thermal strain of CORC cable

Abstract

The invention relates to the technical field of superconducting cables, and discloses a calculation method and device for thermal stress and thermal strain of a CORC cable, and the method comprises the steps: obtaining the cable core inner surface temperature and the cable core outer surface temperature of the CORC cable, and calculating the thermal stress and the thermal strain of the CORC cable based on the cable core inner surface temperature and the cable core outer surface temperature; determining steady-state radial temperature distribution of the cable core by using a heat balance equation of the CORC cable; obtaining a Young modulus, a Poisson's ratio and a thermal expansion coefficient of the cable core functional layer, and determining thermal strain of the CORC cable by using a stress-strain balance equation of the CORC cable based on the steady-state radial temperature distribution, the Young modulus, the Poisson's ratio and the thermal expansion coefficient; and calculating the thermal stress of the CORC cable by using the stress-strain relationship based on the thermal strain of the CORC cable. According to the method, the thermal stress and the thermal strain of the CORC cable are reasonably analyzed, and a scientific basis and an effective means are provided for evaluating the low-temperature shrinkage of the superconducting cable.

Description

Technical Field

[0001] The present invention relates to the technical field of superconducting cables, and in particular to a method and device for calculating thermal stress and thermal strain of a CORC cable. Background Art

[0002] According to the basic characteristics of superconducting materials, superconductors need to be below their critical temperature to be superconducting. 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 material itself and the device-related functional parts and structural parts will be subject to thermal stress and thermal strain caused by low temperature.

[0003] As one of the most widely used superconducting power devices, superconducting cables are particularly susceptible to low-temperature deformation during long-distance power transmission. If the stress and strain of superconducting cables at low temperatures are not evaluated, measures can be taken to compensate for the low-temperature shrinkage of superconducting cables. The core of the superconducting cable will be subjected to great thermal stress, which may damage the cable's conductor and insulation structure, causing the cable to quench or even burn. Therefore, calculating the thermal stress and thermal strain of superconducting cables, especially the CORC (Conductor on round core) structure cables with good heat transfer efficiency, strong flexibility, and friendly electromagnetic environment, is of great value for the application and protection of superconducting cables.

[0004] However, the inability to reasonably analyze and calculate the thermal stress and thermal strain of CORC cables leads to an inaccurate assessment of the low-temperature shrinkage of superconducting cables. Summary of the invention

[0005] In view of this, the present invention provides a method and device for calculating the thermal stress and thermal strain of a CORC cable, so as to solve the problem that the thermal stress and thermal strain of the CORC cable cannot be reasonably calculated analytically.

[0006] In a first aspect, the present invention provides a method for calculating thermal stress and thermal strain of a CORC cable, the method comprising:

[0007] The inner surface temperature and the outer surface temperature of the cable core of the CORC cable are obtained, and based on the inner surface temperature and the outer surface temperature of the cable core, the steady-state radial temperature distribution of the cable core is determined using the heat balance equation of the CORC cable;

[0008] The Young's modulus, Poisson's ratio and thermal expansion coefficient of the cable core functional layer are obtained. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio and thermal expansion coefficient, the thermal strain of the CORC cable is determined using the stress-strain equilibrium equation of the CORC cable. The thermal strain of the CORC cable includes radial strain, hoop strain and axial strain.

[0009] 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, hoop stress and axial stress.

[0010] The present embodiment provides a method for calculating thermal stress and thermal strain of a CORC cable. Based on the inner surface temperature and the outer surface temperature of the cable core, the steady-state radial temperature distribution of the cable core is determined by using the thermal balance equation of the CORC cable. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio and thermal expansion coefficient, the thermal strain of the CORC cable is determined by 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 by using the stress-strain relationship. The method realizes a reasonable analysis of the thermal stress and thermal strain of the CORC cable, avoids the complex modeling and analysis steps and time-consuming calculation process of the numerical simulation method, can reasonably reflect the low-temperature shrinkage degree of the CORC cable, and has a simplified solution process, so as to provide a portable and effective method for compensating the low-temperature shrinkage of the CORC cable, taking into account both technical significance and engineering practical value.

[0011] In an optional embodiment, based on the cable core inner surface temperature and the cable core outer surface temperature, the steady-state radial temperature distribution of the cable core is determined using the heat balance equation of the CORC cable, including:

[0012] The inner surface temperature and the outer surface temperature of the cable core of the CORC cable are obtained, and the heat flux at the radius of the cable core is calculated based on the inner surface temperature and the outer surface temperature of the cable core;

[0013] The steady-state radial temperature distribution is determined based on the heat flux at the cable core radius.

[0014] The present embodiment provides a method for calculating thermal stress and thermal strain of a CORC cable. The heat flux at the radius of the cable core is calculated by the inner surface temperature and the outer surface temperature of the cable core, and then the steady-state radial temperature distribution is determined. The function of temperature and radius is derived by using the heat balance equation of the CORC cable. The influence of the air gap between superconducting tapes and the semi-lapping process, the AC loss of the conductor layer, and the viscous loss of the convection heat transfer surface are ignored. The method has the characteristics of reasonably reflecting the structural characteristics and application conditions of the CORC cable and being easy to solve, and provides a scientific basis and effective means for evaluating the low-temperature shrinkage of superconducting cables.

[0015] In an optional embodiment, the heat flux at the cable core radius is calculated based on the cable core inner surface temperature and the cable core outer surface temperature, including:

[0016] The surface parameters of the cable core functional layer are obtained, and the heat flux at the cable core radius under the Dirichlet boundary condition is calculated based on the cable core inner surface temperature, the cable core outer surface temperature and the cable core functional layer surface parameters;

[0017] Alternatively, 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 are obtained, and the heat flux at the cable core radius under the mixed boundary conditions is calculated based on the inner surface temperature of the cable core, the outer surface temperature of the cable core, the surface parameters of the cable core functional layer, the inner surface heat transfer coefficient of the cable core and the outer surface heat transfer coefficient of the cable core.

[0018] The present embodiment provides a method for calculating thermal stress and thermal strain of a CORC cable, which achieves accurate calculation of the heat flux at the cable core radius in different CORC cable application scenarios by calculating the heat flux at the cable core radius under Dirichlet boundary conditions and mixed boundary conditions.

[0019] In an optional embodiment, 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 thermal expansion coefficient, including:

[0020] 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 thermal expansion coefficient;

[0021] Calculate the radial displacement of the cable core based on multiple recursive constants and the cable core radius;

[0022] The radial strain and the hoop strain are calculated based on the radial displacement of the cable core and the radius of the cable core respectively;

[0023] 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, thermal expansion coefficient and multiple recursive constants;

[0024] Based on the initial axial stress of the cable core, the axial strain is determined using the stress equilibrium condition.

[0025] The present embodiment provides a method for calculating the thermal stress and thermal strain of a CORC cable. A recursive expression is established through stress-strain relationship, strain-displacement relationship, continuity relationship, etc., so as to achieve accurate calculation of the axial strain, radial strain and hoop strain corresponding to the CORC cable, lay a foundation for the subsequent calculation of the thermal stress and thermal strain of the CORC cable, avoid the complex modeling and analysis steps and time-consuming calculation process of the numerical simulation method, and provide a convenient and effective means for the evaluation of low-temperature shrinkage of superconducting cables and the design of related compensation engineering.

[0026] In an optional embodiment, 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 thermal expansion coefficient, including:

[0027] Based on the temperature difference at the cable core radius, Young's modulus, Poisson's ratio and thermal expansion coefficient, the pressure recursion constant is determined by using the radial continuity relationship between displacement and stress at the interface of the cable core functional layer.

[0028] The inner surface pressure of the cable core and the outer surface pressure of the cable core are obtained, and the contact pressure at the interface of the cable core functional layer is calculated based on the inner surface pressure of the cable core, the outer surface pressure of the cable core and the pressure recursion constant;

[0029] The displacement recursion constant is determined based on the contact pressure at the interface of the cable core and the functional layer.

[0030] The present embodiment provides a method for calculating the thermal stress and thermal strain of a CORC cable. The radial continuity relationship between the displacement and stress at the interface of the cable core functional layer is used to determine the pressure recursion constant, and then the contact pressure at the interface of the cable core functional layer is calculated. The displacement recursion constant is determined based on the contact pressure at the interface of the cable core functional layer, and the derivation and calculation of multiple recursion constants are realized, which lays a foundation for the subsequent derivation and calculation of the thermal stress and thermal strain of the CORC cable.

[0031] In an optional embodiment, based on the thermal strain of the CORC cable, the thermal stress of the CORC cable is calculated using the stress-strain relationship, including:

[0032] The thermal stress of the CORC cable is calculated based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio, thermal expansion coefficient, radial strain, hoop strain and axial strain of the cable core. The calculation formula for the thermal stress of the CORC cable is:

[0033]

[0034] in, represents the radial stress, represents the hoop stress, represents the axial stress, represents the radial strain, represents the hoop strain, represents the axial strain, E i represents the Young's modulus of the i-th cable core functional layer, v i represents the Poisson's ratio of the i-th cable core functional layer, α i represents the thermal expansion coefficient of the i-th cable core functional layer, ΔT i (r) represents the temperature difference at the radius r of the cable core.

[0035] In a second aspect, the present invention provides a device for calculating thermal stress and thermal strain of a CORC cable, the device comprising:

[0036] The first determination module is used to obtain the inner surface temperature and the outer surface temperature of the cable core of the CORC cable, and determine the steady-state radial temperature distribution of the cable core by using the heat balance equation of the CORC cable based on the inner surface temperature and the outer surface temperature of the cable core;

[0037] The second determination module is used to obtain the Young's modulus, Poisson's ratio and thermal expansion coefficient of the cable core functional layer, and determine the thermal strain of the CORC cable 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 thermal expansion coefficient; the thermal strain of the CORC cable includes radial strain, hoop strain and axial strain;

[0038] The calculation module is used to calculate the thermal stress of the CORC cable based on the thermal strain of the CORC cable by using the stress-strain relationship; the thermal stress of the CORC cable includes radial stress, hoop stress and axial stress.

[0039] In a third aspect, the present invention provides a computer device, comprising: a memory and a processor, the memory and the processor being communicatively connected to each other, the memory storing computer instructions, and the processor executing the method for calculating thermal stress and thermal strain of a CORC cable according to the first aspect or any corresponding embodiment thereof by executing the computer instructions.

[0040] In a fourth aspect, the present invention provides a computer-readable storage medium having computer instructions stored thereon, the computer instructions being used to enable a computer to execute the method for calculating thermal stress and thermal strain of a CORC cable according to the first aspect or any corresponding embodiment thereof.

[0041] In a fifth aspect, the present invention provides a computer program product, comprising computer instructions for causing a computer to execute the method for calculating thermal stress and thermal strain of a CORC cable according to the first aspect or any corresponding embodiment thereof. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0043] Figure 1 is a flow chart of a method for calculating thermal stress and thermal strain of a CORC cable according to an embodiment of the present invention;

[0044] Figure 2is a flow chart of another method for calculating thermal stress and thermal strain of a CORC cable according to an embodiment of the present invention;

[0045] Figure 3 is a schematic diagram of a composite CORC cable core structure according to an embodiment of the present invention;

[0046] Figure 4 is a flow chart of another method for calculating thermal stress and thermal strain of a CORC cable according to an embodiment of the present invention;

[0047] Figure 5 is a schematic diagram of stress components in a cylindrical coordinate system according to an embodiment of the present invention;

[0048] Figure 6 is a flow chart of a method for calculating thermal stress and thermal strain of a CORC cable based on a recursive method according to an embodiment of the present invention;

[0049] Figure 7 is a comparison diagram of radial thermal strain and annular thermal strain obtained by numerical simulation according to an embodiment of the present invention and calculation results of the recursive method;

[0050] Figure 8 is a comparison diagram of thermal stress in various directions obtained by numerical simulation according to an embodiment of the present invention and calculation results of the recursive method;

[0051] Fig. 9 is a structural block diagram of a device for calculating thermal stress and thermal strain of a CORC cable according to an embodiment of the present invention;

[0052] Fig.10 It is a schematic diagram of the hardware structure of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0054] The method for evaluating the shrinkage degree of superconducting cables at low temperatures generally adopts the empirical formula method, that is, the Dewar tube outside the superconducting cable body is used as a reference, the thermal expansion coefficient is taken from the material parameters of the double-layer stainless steel bellows, and the shrinkage is about 3‰. However, as a composite structure, the geometric parameters and material parameters of each conductor layer and functional layer of the superconducting cable core are different. The empirical formula method uses stainless steel as a reference, and the deformation calculation is inaccurate, and the stress cannot be calculated.

[0055] In addition, numerical simulation methods are used, that is, in finite element simulation software, thermal expansion boundary conditions are used to calculate the thermal stress and thermal strain of the composite structure CORC cable in the superconducting cable during the hot and cold cycle. However, the numerical simulation method also has its shortcomings: first, it is necessary to establish a complex numerical model, including geometry, materials, physical fields and boundary conditions, grids and solver settings, etc. Second, the numerical model usually takes a long time to calculate, especially the spirally wound three-dimensional CORC cable model. The large number of grids has a high hardware requirement for computer simulation calculations, and the non-Cartesian coordinate system makes post-processing more troublesome.

[0056] To solve the above technical problems, an embodiment of the present invention provides a method for calculating the thermal stress and thermal strain of a CORC cable. The calculation of the thermal stress and thermal strain of the CORC cable is divided into two parts: thermal and mechanical. In the thermal part, the radial temperature distribution of the CORC cable in a steady state is calculated through the thermal balance equation, Fourier's law, temperature / heat transfer boundary conditions, etc.; in the mechanical part, a recursive expression is established through the stress-strain relationship, the strain-displacement relationship, the continuity relationship, etc., and then the CORC cable temperature is substituted into the stress-strain expression of each functional layer to obtain the thermal stress and thermal strain of the CORC cable at the current temperature. The thermal stress and thermal strain of the CORC cable in the low-temperature shrinkage process are reasonably considered. The calculation principle is clear, the calculation process is simple and easy to operate, and the calculation result is relatively accurate. The complex modeling and analysis steps and time-consuming calculation process of the numerical simulation method are avoided. It can not only reasonably reflect the low-temperature shrinkage degree of the CORC cable, but also has a simplified solution process. It provides a portable and effective method for compensating the low-temperature shrinkage of the CORC cable, taking into account both technical significance and engineering practical value.

[0057] The embodiment of the present invention provides a method for calculating the thermal stress and thermal strain of a CORC cable. It should be noted that the method for calculating the thermal stress and thermal strain of a CORC cable provided in the embodiment of the present invention may be executed by a device for calculating the thermal stress and thermal strain of a CORC cable. The device for calculating the thermal stress and thermal strain of a CORC cable may be implemented as part or all of an electronic device through software, hardware, or a combination of software and hardware. The electronic device may be a server or a terminal. The server in the embodiment of the present application may be a single server or a server cluster composed of multiple servers. The terminal in the embodiment of the present application may be a smart phone, a personal computer, a tablet computer, a wearable device, an intelligent robot, or other intelligent hardware devices. In the following method embodiments, the execution subject is an electronic device as an example for explanation.

[0058] According to an embodiment of the present invention, an embodiment of a method for calculating thermal stress and thermal strain of a CORC cable is provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0059] In this embodiment, a method for calculating thermal stress and thermal strain of a CORC cable is provided, which can be used in the above-mentioned electronic equipment. Figure 1 is a flow chart of a method for calculating thermal stress and thermal strain of a CORC cable according to an embodiment of the present invention. Figure 1 As shown, the process includes the following steps:

[0060] Step S101, obtaining the inner surface temperature and the outer surface temperature of the cable core of the CORC cable, and determining the steady-state radial temperature distribution of the cable core based on the inner surface temperature and the outer surface temperature of the cable core using the heat balance equation of the CORC cable.

[0061] Specifically, since the two ends of the CORC cable are respectively connected to the superconducting cable terminals, the axial displacement of each functional layer in the cable core is the same. Under the support of the stainless steel bellows skeleton and the tight winding of the protective layer, the interfaces between the functional layers can be regarded as completely bound. Therefore, the influence of the air gap between the superconducting tapes in the conductor layer and the semi-lapping process is ignored, and the spirally wound CORC cable core can be simplified into an axisymmetric composite structure.

[0062] Step S102, obtaining Young's modulus, Poisson's ratio and thermal expansion coefficient of the cable core functional layer, and determining the thermal strain of the CORC cable using the stress-strain equilibrium equation of the CORC cable based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio and thermal expansion coefficient; the thermal strain of the CORC cable includes radial strain, hoop strain and axial strain.

[0063] Step S103, 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, hoop stress and axial stress.

[0064] The present embodiment provides a method for calculating thermal stress and thermal strain of a CORC cable. Based on the inner surface temperature and the outer surface temperature of the cable core, the steady-state radial temperature distribution of the cable core is determined by using the thermal balance equation of the CORC cable. Based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio and thermal expansion coefficient, the thermal strain of the CORC cable is determined by 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 by using the stress-strain relationship. The method realizes a reasonable analysis of the thermal stress and thermal strain of the CORC cable, avoids the complex modeling and analysis steps and time-consuming calculation process of the numerical simulation method, can reasonably reflect the low-temperature shrinkage degree of the CORC cable, and has a simplified solution process, so as to provide a portable and effective method for compensating the low-temperature shrinkage of the CORC cable, taking into account both technical significance and engineering practical value.

[0065] In this embodiment, a method for calculating thermal stress and thermal strain of a CORC cable is provided, which can be used in the above-mentioned electronic equipment. Figure 2 is a flow chart of a method for calculating thermal stress and thermal strain of a CORC cable according to an embodiment of the present invention. Figure 2 As shown, the process includes the following steps:

[0066] Step S201, obtaining the inner surface temperature and the outer surface temperature of the cable core of the CORC cable, and determining the steady-state radial temperature distribution of the cable core based on the inner surface temperature and the outer surface temperature of the cable core using the heat balance equation of the CORC cable.

[0067] Specifically, the above step S201 includes:

[0068] Step S2011, obtaining the cable core inner surface temperature and the cable core outer surface temperature of the CORC cable, and calculating the heat flux at the cable core radius based on the cable core inner surface temperature and the cable core outer surface temperature.

[0069] Specifically, when the temperatures of the inner and outer surfaces of the cable core are obtained (temperature measurements are taken inside and outside the cable), the heat flux at the cable core radius under the Dirichlet boundary condition is calculated; the physical properties of the cable core material and the refrigerant (liquid nitrogen) are obtained, and the heat flux at the cable core radius under the mixed boundary condition is calculated; different boundary conditions can be selected according to the situation.

[0070] In some optional implementations, the above step S2011 includes:

[0071] Step a1, obtaining the surface parameters of the cable core functional layer, and calculating the heat flux at the cable core radius under the Dirichlet boundary condition based on the cable core inner surface temperature, the cable core outer surface temperature and the cable core functional layer surface parameters.

[0072] Specifically, the composite CORC cable core structure is as follows: Figure 3As shown in the figure, from the inner layer to the outer layer, the surface parameters of the cable core functional layer include: the radius, temperature and thermal conductivity of each cable core functional layer surface are r i , T i and k i ,i=0,1,2,…,N;T i is the inner surface temperature of the cable core; h i is the convection heat transfer coefficient of the inner surface of the cable core; p0 is the pressure on the inner surface of the cable core; T o is the cable core outer surface temperature; h o is the convection heat transfer coefficient of the cable core surface; p N is the outer surface pressure of the cable core.

[0073] Furthermore, in cylindrical coordinates, the general form of the heat conduction equation is:

[0074]

[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 radial, circumferential and axial coordinates respectively, ρ i is the density of the i-th functional layer, c i is the specific heat capacity of the i-th functional layer, and t is the time operator.

[0076] Furthermore, for superconducting cables, the heat source in the cable core only includes the AC loss of the conductor layer and the viscous loss of the convection heat transfer surface, which can be ignored. Therefore, the heat conduction equation of the i-th layer in steady state can be simplified to:

[0077]

[0078] Furthermore, according to the above formula (2), the heat flux q(r) at the cable core radius r is calculated using Fourier's law:

[0079]

[0080] Furthermore, when the temperature of the inner and outer surfaces of the cable core is constant, or the convective heat transfer coefficient between the inner and outer surfaces of the cable core and liquid nitrogen tends to infinity, the heat flux of the CORC cable core at the cable core radius r under the Dirichlet boundary condition is:

[0081]

[0082] Step a2, alternatively, 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 cable core radius 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 cable core functional layer, the inner surface heat transfer coefficient of the cable core and the outer surface heat transfer coefficient of the cable core.

[0083] Specifically, for mixed boundary conditions, the heat transfer coefficient of the inner surface of the cable core h i and the heat transfer coefficient of the cable core outer surface h o , calculate the heat flux q(r) at the cable core radius r, and the calculation formula is as follows:

[0084]

[0085] Step S2012, determining the steady-state radial temperature distribution based on the heat flux at the cable core radius.

[0086] Specifically, according to the heat flux q(r) at the cable core radius r, without considering the accumulation or dissipation of heat, the steady-state radial temperature distribution of the cable core is obtained by integrating along the cable core radius r. The steady-state radial temperature distribution of the cable core can be expressed as:

[0087]

[0088] Step S202, obtain the Young's modulus, Poisson's ratio and thermal expansion coefficient of the cable core functional layer, and determine the thermal strain of the CORC cable 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 thermal expansion coefficient; the thermal strain of the CORC cable includes radial strain, hoop strain and axial strain. For details, please refer to Figure 1 Step S102 of the illustrated embodiment will not be described in detail here.

[0089] Step S203, 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, hoop stress and axial stress. Figure 1 Step S103 of the illustrated embodiment will not be described in detail here.

[0090] The present embodiment provides a method for calculating thermal stress and thermal strain of a CORC cable. The heat flux at the radius of the cable core is calculated by the inner surface temperature and the outer surface temperature of the cable core, and then the steady-state radial temperature distribution is determined. The function of temperature and radius is derived by using the heat balance equation of the CORC cable. The influence of the air gap between superconducting tapes and the semi-lapping process, the AC loss of the conductor layer, and the viscous loss of the convection heat transfer surface are ignored. The method has the characteristics of reasonably reflecting the structural characteristics and application conditions of the CORC cable and being easy to solve, and provides a scientific basis and effective means for evaluating the low-temperature shrinkage of superconducting cables.

[0091] In this embodiment, a method for calculating thermal stress and thermal strain of a CORC cable is provided, which can be used in the above-mentioned electronic equipment. Figure 4 is a flow chart of a method for calculating thermal stress and thermal strain of a CORC cable according to an embodiment of the present invention. Figure 4 As shown, the process includes the following steps:

[0092] Step S401, obtaining the inner surface temperature and outer surface temperature of the cable core of the CORC cable, and determining the steady-state radial temperature distribution of the cable core using the heat balance equation of the CORC cable based on the inner surface temperature and the outer surface temperature of the cable core. Figure 2 Step S201 of the illustrated embodiment will not be described in detail here.

[0093] Step S402, obtaining Young's modulus, Poisson's ratio and thermal expansion coefficient of the cable core functional layer, and determining the thermal strain of the CORC cable using the stress-strain equilibrium equation of the CORC cable based on the steady-state radial temperature distribution, Young's modulus, Poisson's ratio and thermal expansion coefficient; the thermal strain of the CORC cable includes radial strain, hoop strain and axial strain.

[0094] Specifically, Figure 5 As shown in Figure 2, for the axial shrinkage of the cable at low temperature, 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, the axial strain of the cable core is assumed to be 0.

[0095] The above step S402 includes:

[0096] Step S4021, determining the temperature difference at the cable core radius based on the steady-state radial temperature distribution of the cable core, and deriving and calculating multiple recursive constants based on the temperature difference at the cable core radius, Young's modulus, Poisson's ratio and thermal expansion coefficient.

[0097] Specifically, the temperature difference at the cable core radius is the temperature T at the cable core radius r. i (r) and the initial reference temperature T ref The difference.

[0098] Furthermore, assuming that the interface between the cable core and the functional layer is completely bound, the recursive constant δ in the pressure expression is determined by the radial continuity relationship between the displacement and stress at the interface between the cable core and the functional layer: i+1 , C i , D i and F i , and then based on the constants G0, G1, H0 and H1, determine the recursive constant G in the pressure expression i and H i .

[0099] In some optional implementations, the above step S4021 includes:

[0100] Step b1, based on the temperature difference at the cable core radius, Young's modulus, Poisson's ratio and thermal expansion coefficient, the pressure recursion constant is determined by using the radial continuity relationship between the displacement and stress at the interface of the cable core functional layer.

[0101] Specifically, the stress-strain relationship of the i-th layer of anisotropic material is:

[0102]

[0103] Where, ΔT i (r) is 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 the initial reference temperature T ref The difference, E i represents the Young's modulus of the i-th cable core functional layer, v i represents the Poisson's ratio of the i-th cable core functional layer, α i represents the thermal expansion coefficient of the i-th cable core functional layer, σ and ε represent stress and strain respectively, the subscripts rr, θθ and zz represent radial, circumferential and axial directions respectively, and the superscript i represents the i-th cable core functional layer.

[0104] Furthermore, under axisymmetric load, the stress and strain of the cable core are independent of the annular coordinate θ, while the radial displacement and axial displacement depend only on their corresponding coordinates. Therefore, the simplified strain-displacement relationship of the i-th layer of the cable core in the cylindrical coordinate system can be expressed as:

[0105]

[0106] in, Represents the radial displacement of the i-th cable core functional layer.

[0107] Furthermore, since the stress of the cable core is independent of the axial coordinate z, the equilibrium equation of the radial stress and the hoop stress of the i-th layer of the cable core is:

[0108]

[0109] Furthermore, by substituting the above formula (8) into formula (7) and then into formula (9), the stress equilibrium equation expressed by displacement is obtained as follows:

[0110]

[0111] Furthermore, the above formula is integrated along the cable core radius r, and the radial displacement of the cable core is:

[0112]

[0113] Among them, the intermediate parameter I corresponding to the i-th cable core functional layer i (r), β i and γ i It can be expressed as:

[0114]

[0115] Furthermore, since it is assumed that the interfaces between the functional layers are completely bound, the radial displacement and radial stress at the interfaces between the functional layers of each cable core are continuous. Therefore, the radial continuity relationship at the interfaces between the functional layers of the cable core is:

[0116]

[0117] Further, according to the above formula (12) I i Definition of (r), I i+1 (r i ) is 0, so the displacement recursion constant A in the cable core radial displacement expression is i+1 and B i+1 for:

[0118]

[0119] Furthermore, in order to determine the constant A in the above formula i+1 and B i+1 , the radial stress at the interface of the cable core functional layer represented by the contact pressure is:

[0120]

[0121] According to the above formula (15), the pressure recursion constant δ i+1 , C i , D i and F i It can be expressed as:

[0122]

[0123] Furthermore, according to the radial stress at the interface of the cable core functional layer represented by the contact pressure, the contact pressure on the outer surface of the i-th layer of the cable core is:

[0124]

[0125] Furthermore, the displacement recursion constant A in the above formula (15) is i and B i Substituting into the above formula (17), the contact pressure at the interface of the cable core functional layer is:

[0126]

[0127] Further, simplifying the above formula (18), the contact pressure at the interface of the cable core functional layer can be expressed by the following formula:

[0128] p i+1 =G i+1 p1+H i+1 p0 (19)

[0129] Where p0 is the pressure on the inner surface of the cable core, and the pressure recursion constant G is i+1 and H i+1 It can be expressed as:

[0130]

[0131] In the above formula, G0=0, G1=1, H0=1, H1=0.

[0132] Step b2, obtaining the cable core inner surface pressure and the cable core outer surface pressure, and calculating the contact pressure at the interface of the cable core functional layer based on the cable core inner surface pressure, the cable core outer surface pressure and the pressure recursion constant.

[0133] Specifically, the inner surface pressure p0 and the outer surface pressure p N , the contact pressure at each interface of the cable core is calculated by the general formula of the pressure expression, that is, when i = N-1, the calculation formula of the contact pressure p1 at the interface of the cable core functional layer is:

[0134]

[0135] In the formula, p N is the outer surface pressure of the cable core.

[0136] Furthermore, due to the inner surface pressure p0 and outer surface pressure p N can be measured using the cable cryogenic system. Therefore, the contact pressure p at the interface of the cable core functional layer is i It can be determined by the following recursive relationship:

[0137]

[0138] Step b3, determining the displacement recursion constant based on the contact pressure at the interface of the cable core functional layer.

[0139] Specifically, the contact pressure p at the interface of the cable core functional layer is i Substituting into the above formula (15), we get the displacement recursion constant, displacement recursion constant A i and B i It can be expressed as:

[0140]

[0141] Step S4022, calculating the radial displacement of the cable core based on multiple recursive constants and the cable core radius.

[0142] Specifically, the displacement recursion constant A is i and B i , calculate the radial displacement of the cable core at the cable core radius r, and the calculation formula is as follows:

[0143]

[0144] Step S4023, respectively calculating radial strain and hoop strain based on the cable core radial displacement and the cable core radius.

[0145] Specifically, the radial strain of the cable core is calculated from the strain-displacement relationship in the above formula (8): and hoop strain

[0146] Step S4024, determining the initial axial stress of the cable core based on the temperature difference at the cable core radius, Young's modulus, Poisson's ratio, thermal expansion coefficient and multiple recursive constants.

[0147] Specifically, assuming that the axial strain of the cable core is 0, the calculation formula for the initial axial stress of the cable core is as follows:

[0148]

[0149] Step S4025, based on the initial axial stress of the cable core, the axial strain is determined using the stress equilibrium condition.

[0150] Specifically, considering the axial contraction of the cable under thermal-mechanical load, the axial external load F z , calculate the axial strain of the cable core, that is, according to the stress equilibrium condition, that is, the axial resultant force on the cable end face is equal to the external load, the true axial strain of the cable core is:

[0151]

[0152] Step S403, 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, hoop stress and axial stress.

[0153] Specifically, the thermal stress of the CORC cable is calculated based on the steady-state radial temperature distribution of the cable core, Young's modulus, Poisson's ratio, thermal expansion coefficient, radial strain, hoop strain and axial strain.

[0154] Furthermore, from the basic knowledge of engineering mechanics, it can be known that when the axial strain of the cable is 0 and the cable responds to the external axial load, in the absence of loads in other directions, the mechanical behavior is uniaxial tension. Therefore, the axial strain and hoop strain of the cable core remain unchanged. According to the stress-strain relationship, the true stress of the cable core under thermal-mechanical load is:

[0155]

[0156] in, represents the radial stress, represents the hoop stress, represents the axial stress, represents the radial strain, represents the hoop strain, represents the axial strain, E i represents the Young's modulus of the i-th cable core functional layer, v i represents the Poisson's ratio of the i-th cable core functional layer, α i represents the thermal expansion coefficient of the i-th cable core functional layer, ΔT i (r) represents the temperature difference at the radius r of the cable core.

[0157] The present embodiment provides a method for calculating the thermal stress and thermal strain of a CORC cable. A recursive expression is established through stress-strain relationship, strain-displacement relationship, continuity relationship, etc., so as to achieve accurate calculation of the axial strain, radial strain and hoop strain corresponding to the CORC cable, lay a foundation for the subsequent calculation of the thermal stress and thermal strain of the CORC cable, avoid the complex modeling and analysis steps and time-consuming calculation process of the numerical simulation method, and provide a convenient and effective means for the evaluation of low-temperature shrinkage of superconducting cables and the design of related compensation engineering.

[0158] The following is a specific example to illustrate the steps and beneficial effects of a method for calculating thermal stress and thermal strain of a CORC cable.

[0159] Embodiment 1:

[0160] like Figure 6 As shown, the steps of the method for calculating the thermal stress and thermal strain of the CORC cable include:

[0161] Step 1001: For the Dirichlet boundary condition, the temperature of the inner surface of the cable core T i and the outer surface temperature T o , calculate the heat flux at the cable core radius r;

[0162] Step 1002: For mixed boundary conditions, the heat transfer coefficient h of the inner surface of the cable core is i and the external surface heat transfer coefficient h o , calculate the heat flux at the cable core radius r;

[0163] Step 1003: Based on the calculated heat flux q(r), without considering the accumulation or dissipation of heat, the steady-state radial temperature distribution of the cable core is obtained by integrating along the cable core radius r;

[0164] Step 1004: Assuming that the interface between the cable core functional layer is completely bound, the pressure recursion constant δ in the pressure expression is determined based on the radial continuity relationship between the displacement and stress at the interface between the cable core functional layer. i+1 , C i , D i and F i ;

[0165] Step 1005: Based on constants G0, G1, H0 and H1, determine the pressure recursive constant G in the general formula of the pressure expression i and H i ;

[0166] Step 1006: The inner surface pressure p0 and the outer surface pressure p N , the contact pressure at the interface of the cable core functional layer is calculated by the general formula of the pressure expression;

[0167] Step 1007: Determine the displacement recursion constant A in the radial displacement expression i and B i ;

[0168] Step 1008: Derivation of constant A by displacement recursion i and B i , calculate the radial displacement at the cable core radius r;

[0169] Step 1009: Further, the radial strain and the hoop strain of the cable core are calculated from the strain-displacement relationship;

[0170] Step 1010: Calculate the axial stress of the cable core based on the assumption that the axial strain of the cable core is 0;

[0171] Step 1011: Consider the axial contraction of the cable under thermal-mechanical loads by using the axial external load F z , calculate the axial strain of the cable core;

[0172] Step 1012: Finally, the true radial stress, hoop stress and axial stress of the cable core are calculated by the calculated axial strain and the stress-strain relationship.

[0173] Embodiment 2:

[0174] Select the geometric and material parameters of a 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 that the temperature difference between the inner and outer surfaces is 70K, and the pressures of the inner and outer surfaces are 22MPa and 1.5MPa respectively, where the geometric and material parameter settings are shown in Table 1 below:

[0175] Table 1:

[0176] layer <![CDATA[r i-1 / mm]]> <![CDATA[r i / mm]]> <![CDATA[E i / GPa]]> <![CDATA[v i / 1]]> <![CDATA[α i / K -1 ]]> <![CDATA[k i / World Cup -1 K -1 ]]> 1 500 510 190 0.28 <![CDATA[18.7×10 -6 ]]> 18.4 2 510 520 194 0.28 <![CDATA[17.4×10 -6 ]]> 25.4 3 520 530 198 0.28 <![CDATA[16.1×10 -6 ]]> 32.4 4 530 540 202 0.28 <![CDATA[14.8×10 -6 ]]> 39.4 5 540 550 206 0.28 <![CDATA[13.5×10 -6 ]]> 46.4 6 550 580 210 0.3 <![CDATA[12.2×10 -6 ]]> 53.4

[0177] The commercial software COMSOL Multiphysics was used to perform numerical simulation analysis on the above example, and the thermal stress and thermal strain were calculated through thermal expansion.

[0178] Figure 7 The comparison diagram of the radial thermal strain and circumferential thermal strain of each point in the radial direction of the embodiment obtained by numerical simulation and the calculation results of the thermal stress and strain of the CORC cable based on the recursive method is shown in the figure. Figure 8 The thermal stress of each point in each direction in the radial direction of the embodiment obtained by numerical simulation is compared with the calculation results of the thermal stress and strain of the CORC cable based on the recursive method; Figure 7 , Figure 8 As shown, the distribution curves of the two are relatively close and have basically the same change characteristics.

[0179] In addition, the maximum relative error of the calculation results of radial displacement between numerical simulation and the calculation method of thermal stress and strain of CORC cable based on recursion method is 0.55%, and the maximum relative error of hoop strain is 0.6%. It should be noted that the calculation method of thermal stress and strain of CORC cable based on recursion method first assumes that the initial axial strain is 0, and describes the mechanical behavior of the material under external load by uniaxial tension, that is, the real axial strain of the composite model is calculated according to the stress equilibrium condition, ignoring the effect of axial stress on radial strain and hoop strain, which is one of the main reasons for the deviation from the numerical simulation calculation results.

[0180] In the above embodiment, in the calculation process of the thermal stress and strain of the CORC cable, the thermodynamic concept is clear and the derivation is rigorous. The function of temperature and radius is derived through the thermal balance equation of the CORC cable, and the recursive equation of the interface pressure, radial displacement, strain and stress is derived through the stress-strain balance equation of the CORC cable to determine the thermal stress and thermal strain of the CORC cable at the current temperature; at the same time, the influence of the air gap between the superconducting tapes and the half-lapping process, the AC loss of the conductor layer and the viscous loss of the convection heat transfer surface are ignored, which has the characteristics of both reasonably reflecting the structural characteristics and application conditions of the CORC cable and being easy to solve, and provides a scientific basis and effective means for the evaluation of the low-temperature shrinkage of the superconducting cable; finally, the thermal stress and thermal strain of the CORC cable are calculated by a simple calculation program in a quick way, the calculation process is simple, the calculation time is short, and the result is relatively accurate, which avoids the complex modeling and analysis steps and time-consuming calculation process of the numerical simulation method, and provides a convenient and effective means for the evaluation of the low-temperature shrinkage of the superconducting cable and the design of related compensation engineering.

[0181] In this embodiment, a device for calculating the thermal stress and thermal strain of a CORC cable is also provided, and the device is used to implement the above-mentioned embodiments and preferred implementation modes, and the descriptions that have been made are not repeated. As used below, the term "module" can be a combination of software and / or hardware that implements a predetermined function. Although the device described in the following embodiments is preferably implemented in software, the implementation of hardware, or a combination of software and hardware, is also possible and conceivable.

[0182] This embodiment provides a device for calculating the thermal stress and thermal strain of a CORC cable. Fig. 9 As shown, including:

[0183] The first determination module 901 is used to obtain the inner surface temperature and the outer surface temperature of the cable core of the CORC cable, and determine the steady-state radial temperature distribution of the cable core based on the inner surface temperature and the outer surface temperature of the cable core by using the heat balance equation of the CORC cable;

[0184] The second determination module 902 is used to obtain the Young's modulus, Poisson's ratio and thermal expansion coefficient of the cable core functional layer, and determine the thermal strain of the CORC cable 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 thermal expansion coefficient; the thermal strain of the CORC cable includes radial strain, hoop strain and axial strain;

[0185] The calculation module 903 is used to calculate the thermal stress of the CORC cable based on the thermal strain of the CORC cable by using the stress-strain relationship; the thermal stress of the CORC cable includes radial stress, hoop stress and axial stress.

[0186] In some optional implementations, the first determining module 901 includes:

[0187] The first calculation unit is used to obtain the inner surface temperature of the cable core and the outer surface temperature of the cable core of the CORC cable, and calculate the heat flux at the radius of the cable core based on the inner surface temperature of the cable core and the outer surface temperature of the cable core;

[0188] The first determining unit is used to determine the steady-state radial temperature distribution based on the heat flux at the cable core radius.

[0189] In some optional implementations, the first computing unit includes:

[0190] 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 condition based on the cable core inner surface temperature, the cable core outer surface temperature and the cable core functional layer surface parameters;

[0191] The second calculation subunit is used to 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 cable core radius under the 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 cable core functional layer, the inner surface heat transfer coefficient of the cable core and the outer surface heat transfer coefficient of the cable core.

[0192] In some optional implementations, the second determining module 902 includes:

[0193] A 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 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 thermal expansion coefficient;

[0194] A third calculation unit, used for calculating the radial displacement of the cable core based on a plurality of recursive constants and the cable core radius;

[0195] A fourth calculation unit, used for respectively calculating radial strain and hoop strain based on the radial displacement of the cable core and the radius of the cable core;

[0196] A second determination 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, thermal expansion coefficient and a plurality of recursive constants;

[0197] The third determining unit is used to determine the axial strain based on the initial axial stress of the cable core and using the stress balance condition.

[0198] In some optional implementations, the second computing unit includes:

[0199] The first determination subunit is used to determine the pressure recursion constant based on the temperature difference at the cable core radius, Young's modulus, Poisson's ratio and thermal expansion coefficient, and by using the radial continuity relationship between the displacement and stress at the interface of the cable core functional layer;

[0200] The third calculation subunit is used to obtain the pressure on the inner surface of the cable core and the pressure on the outer surface of the cable core, and calculate the contact pressure at the interface of the cable core functional layer based on the pressure on the inner surface of the cable core, the pressure on the outer surface of the cable core and the pressure recursion constant;

[0201] The second determination subunit is used to determine the displacement recursion constant based on the contact pressure at the interface of the cable core functional layer.

[0202] In some optional embodiments, 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, thermal expansion coefficient, radial strain, hoop strain and axial strain of the cable core. The calculation formula of the thermal stress of the CORC cable is:

[0203]

[0204] in, represents the radial stress, represents the hoop stress, represents the axial stress, represents the radial strain, represents the hoop strain, represents the axial strain, E i represents the Young's modulus of the i-th cable core functional layer, v i represents the Poisson's ratio of the i-th cable core functional layer, α i represents the thermal expansion coefficient of the i-th cable core functional layer, ΔT i (r) represents the temperature difference at the radius r of the cable core.

[0205] The further functional description of each of the above modules and units is the same as that of the above corresponding embodiments and will not be repeated here.

[0206] In this embodiment, a device for calculating thermal stress and thermal strain of a CORC cable is presented in the form of a functional unit, where the unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and memory that executes one or more software or fixed programs, and / or other devices that can provide the above functions.

[0207] The embodiment of the present invention also provides a computer device having the above Fig. 9 A device for calculating thermal stress and thermal strain of a CORC cable is shown.

[0208] See also Fig.10 , Fig.10 is a schematic diagram of the structure of a computer device provided by an optional embodiment of the present invention, such as Fig.10 As shown, the computer device includes: one or more processors 10, a memory 20, and interfaces for connecting various components, including high-speed interfaces and low-speed interfaces. Various components are connected to each other using different buses for communication, and can be installed on a common mainboard or installed in other ways as needed. The processor can process instructions executed in the computer device, including instructions stored in or on the memory to display the graphical information of the GUI on an external input / output device (such as a display device coupled to the interface). In some optional embodiments, if necessary, multiple processors and / or multiple buses can be used together with multiple memories. Similarly, multiple computer devices can be connected, and each device provides some necessary operations (for example, as a server array, a group of blade servers, or a multi-processor system). Fig.10 A processor 10 is taken as an example.

[0209] The processor 10 may be a central processing unit, a network processor or a combination thereof. The processor 10 may further include a hardware chip. The hardware chip may be a dedicated integrated circuit, a programmable logic device or a combination thereof. The programmable logic device may be a complex programmable logic device, a field programmable gate array, a general purpose array logic or any combination thereof.

[0210] The memory 20 stores instructions executable by at least one processor 10, so that the at least one processor 10 executes the method shown in the above embodiment.

[0211] The memory 20 may include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application required for at least one function; the data storage area may store data created according to the use of the computer device, etc. In addition, the memory 20 may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some optional embodiments, the memory 20 may optionally include a memory remotely arranged relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0212] The memory 20 may include a volatile memory, such as a random access memory; the memory may also include a non-volatile memory, such as a flash memory, a hard disk or a solid state drive; the memory 20 may also include a combination of the above types of memory.

[0213] The computer device further comprises a communication interface 30 for the computer device to communicate with other devices or a communication network.

[0214] The embodiment of the present invention also provides a computer-readable storage medium. The method according to the embodiment of the present invention can be implemented in hardware, firmware, or can be implemented as a computer code that can be recorded in a storage medium, or can be implemented as a computer code that is originally stored in a remote storage medium or a non-temporary machine-readable storage medium and will be stored in a local storage medium through a network download, so that the method described herein can be stored in such software processing on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only storage memory, a random access memory, a flash memory, a hard disk or a solid-state hard disk, etc.; further, the storage medium can also include a combination of the above types of memories. It can be understood that a computer, a processor, a microprocessor controller, or programmable hardware includes a storage component that can store or receive software or computer code. When the software or computer code is accessed and executed by a computer, a processor, or hardware, the method shown in the above embodiment is implemented.

[0215] A part of the present invention may be applied as a computer program product, such as a computer program instruction, which, when executed by a computer, can call or provide the method and / or technical solution according to the present invention through the operation of the computer. Those skilled in the art should understand that the existence of the computer program instruction in a computer-readable medium includes, but is not limited to, a source file, an executable file, an installation package file, etc., and accordingly, the way in which the computer program instruction is executed by the computer includes, but is not limited to: the computer directly executes the instruction, or the computer compiles the instruction and then executes the corresponding compiled program, or the computer reads and executes the instruction, or the computer reads and installs the instruction and then executes the corresponding installed program. Here, the computer-readable medium may be any available computer-readable storage medium or communication medium accessible to the computer.

[0216] Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations are all within the scope defined by the appended claims.

Claims

1. A method for calculating thermal stress and thermal strain of a CORC cable, characterized in that: The method comprises: Acquire the inner surface temperature and the outer surface temperature of the cable core of the CORC cable, and determine the steady-state radial temperature distribution of the cable core by using the heat balance equation of the CORC cable based on the inner surface temperature and the outer surface temperature of the cable core; Obtaining Young's modulus, Poisson's ratio and thermal expansion coefficient of the cable core functional layer, and determining the thermal strain of the CORC cable using the stress-strain balance equation of the CORC cable based on the steady-state radial temperature distribution, the Young's modulus, the Poisson's ratio and the thermal expansion coefficient; the thermal strain of the CORC cable includes radial strain, hoop 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, hoop stress and axial stress.

2. The method according to claim 1, characterized in that The method of determining the steady-state radial temperature distribution of the cable core based on the cable core inner surface temperature and the cable core outer surface temperature by using the heat balance equation of the CORC cable comprises: Acquire the cable core inner surface temperature and the cable core outer surface temperature of the CORC cable, and calculate the heat flux at the cable core radius based on the cable core inner surface temperature and the cable core outer surface temperature; The steady-state radial temperature distribution is determined based on the heat flux at the cable core radius.

3. The method according to claim 2, characterized in that The step of calculating the heat flux at the cable core radius based on the cable core inner surface temperature and the cable core outer surface temperature comprises: Acquire the surface parameters of the cable core functional layer, and calculate the heat flux at the cable core radius under the Dirichlet boundary condition based on the cable core inner surface temperature, the cable core outer surface temperature and the cable core functional layer surface parameters; Alternatively, 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 are obtained, and the heat flux at the radius of the cable core under mixed boundary conditions is calculated based on the inner surface temperature of the cable core, the outer surface temperature of the cable core, the surface parameters of the cable core functional layer, the inner surface heat transfer coefficient of the cable core and the outer surface heat transfer coefficient of the cable core.

4. The method according to claim 1, characterized in that The method of determining the thermal strain of the CORC cable by using the stress-strain balance equation of the CORC cable based on the steady-state radial temperature distribution, the Young's modulus, the Poisson's ratio and the thermal expansion coefficient comprises: 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 a plurality of recursive constants based on the temperature difference at the radius of the cable core, the Young's modulus, the Poisson's ratio and the thermal expansion coefficient; Calculating the radial displacement of the cable core based on the multiple recursion constants and the cable core radius; Calculate the radial strain and the hoop strain respectively based on the cable core radial displacement and the cable core radius; Determining an initial axial stress of the cable core based on the temperature difference at the cable core radius, the Young's modulus, the Poisson's ratio, the thermal expansion coefficient, and the plurality of recursion constants; The axial strain is determined based on the initial axial stress of the cable core using a stress equilibrium condition.

5. The method according to claim 4, characterized in that The method of determining the temperature difference at the radius of the cable core based on the steady-state radial temperature distribution of the cable core, and deriving and calculating a plurality of recursive constants based on the temperature difference at the radius of the cable core, the Young's modulus, the Poisson's ratio and the thermal expansion coefficient, comprises: Based on the temperature difference at the cable core radius, the Young's modulus, the Poisson's ratio and the thermal expansion coefficient, the pressure recursion constant is determined by utilizing the radial continuity relationship between the displacement and stress at the interface of the cable core functional layer; Obtaining the cable core inner surface pressure and the cable core outer surface pressure, and calculating the contact pressure at the interface of the cable core functional layer based on the cable core inner surface pressure, the cable core outer surface pressure and the pressure recursion constant; The displacement recursion constant is determined based on the contact pressure at the interface of the cable core functional layer.

6. The method according to claim 1, characterized in that The method of calculating the thermal stress of the CORC cable based on the thermal strain of the CORC cable by using a stress-strain relationship comprises: 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 thermal expansion coefficient, the radial strain, the hoop strain and the axial strain. The calculation formula of the thermal stress of the CORC cable is: in, represents the radial stress, represents the hoop stress, represents the axial stress, represents the radial strain, represents the hoop strain, represents the axial strain, E i represents the Young's modulus of the i-th cable core functional layer, v i represents the Poisson's ratio of the i-th cable core functional layer, α i represents the thermal expansion coefficient of the i-th cable core functional layer, ΔT i (r) represents the temperature difference at the radius r of the cable core.

7. A device for calculating thermal stress and thermal strain of a CORC cable, characterized in that: The device comprises: A first determination module is used to obtain the inner surface temperature of the cable core and the outer surface temperature of the cable core of the CORC cable, and determine the steady-state radial temperature distribution of the cable core by using the heat balance equation of the CORC cable based on the inner surface temperature of the cable core and the outer surface temperature of the cable core; The second determination module is used to obtain the Young's modulus, Poisson's ratio and thermal expansion coefficient of the cable core functional layer, and determine the thermal strain of the CORC cable using the stress-strain balance equation of the CORC cable based on the steady-state radial temperature distribution, the Young's modulus, the Poisson's ratio and the thermal expansion coefficient; the thermal strain of the CORC cable includes radial strain, hoop strain and axial strain; A calculation module is used to calculate the thermal stress of the CORC cable based on the thermal strain of the CORC cable by using the stress-strain relationship; the thermal stress of the CORC cable includes radial stress, hoop stress and axial stress.

8. A computer device, characterized in that: include: A memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the method for calculating thermal stress and thermal strain of the CORC cable according to any one of claims 1 to 6 by executing the computer instructions.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a computer to execute the method for calculating thermal stress and thermal strain of a CORC cable according to any one of claims 1 to 6.

10. A computer program product, characterized in that The invention comprises computer instructions for causing a computer to execute the method for calculating thermal stress and thermal strain of a CORC cable according to any one of claims 1 to 6.

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