Quenching characterization method and device for multi-field coupling of high-temperature superconducting coated conductor and medium

Abstract

The invention discloses a quench characterization method and device for multi-field coupling of a high-temperature superconducting coating conductor and a medium, and relates to the technical field of superconducting strips. The method comprises the following steps: establishing a force-electricity-heat multi-physics field coupling model; the force-electricity-heat multi-physics field coupling model comprises an electricity module, a mechanical module and a thermal module; in the electrical module and the thermal module, the material conductivity is a function of temperature, and Joule heat causes temperature change, so that electric-thermal bidirectional coupling is realized; in the thermal module and the mechanical module, temperature change enables the strip to generate thermal strain, a strain item exists in a non-classical Fourier heat conduction equation based on the generalized thermoelasticity principle, and force-heat bidirectional coupling is achieved. According to the method, a mixed dimension model is adopted, a superconducting layer is modeled into a two-dimensional plane, a silver layer and a buffer layer are geometrically ignored, interlayer contact resistance and thermal resistance are added through weak contribution, and the quench process of multi-field coupling of the high-temperature superconducting coating conductor is successfully simulated.

Description

Technical Field

[0001] The present invention relates to the technical field of superconducting tapes, and more particularly, to a method, device and medium for characterizing the quench of a high-temperature superconducting coated conductor under multi-field coupling. Background Art

[0002] High-temperature superconducting tapes are widely used in various fields due to their good current-carrying capacity. However, commercially available or industrially produced high-temperature superconducting tapes may generate thermal disturbances due to internal defects, thereby triggering a quench. High-temperature superconducting devices usually operate in extreme environments. Traditional quench detection methods based on temperature and voltage are subject to interference, resulting in untimely detection. Moreover, the slow quench propagation speed of high-temperature superconducting tapes makes timely quench detection and protection particularly difficult, which often causes damage and burnout of superconducting devices. In order to detect the quench of high-temperature superconducting tapes in a timely manner, it is necessary to develop a quench detection scheme based on strain and strain rate. Summary of the Invention

[0003] To solve the above technical problems, the present invention provides a method, device and medium for characterizing the quench of a high-temperature superconducting coated conductor under multi-field coupling. By using the COMSOL finite element simulation software, a multi-field coupling model of force-electricity-thermal quench of high-temperature superconducting tapes is developed. A mixed-dimensional model is adopted, and the interlayer contact resistance and thermal resistance are added through weak contributions. By using the generalized thermoelasticity principle, the quench process of the high-temperature superconducting coated conductor under multi-field coupling is successfully simulated, and the effective characterization of multiple fields and multiple variables during the quench process of the tape is realized.

[0004] In a first aspect, the present invention provides a method for characterizing the quench of a high-temperature superconducting coated conductor under multi-field coupling, the method comprising:

[0005] Establishing a multi-physical field coupling model of force, electricity and heat; wherein, the multi-physical field coupling model of force, electricity and heat includes an electrical module, a mechanical module and a thermal module;

[0006] In the electrical module and the thermal module, the material conductivity is a function of temperature, and the joule heat causes a temperature change, thereby realizing the two-way coupling of electricity and heat;

[0007] In the thermal module and the mechanical module, the temperature causes thermal strain in the tape, and there is a strain term in the non-classical Fourier heat conduction equation adopted by the temperature field, realizing the two-way coupling of force and heat.

[0008] Further, the electrical module is established by the following method:

[0009] Modeling the copper layer and the NI substrate as three-dimensional, and the superconducting layer as a two-dimensional thin shell. Geometrically, the silver layer and the buffer layer are ignored, and only their contact resistance effects are considered electrically. The three-dimensional control equation of the electric field is determined as:

[0010]

[0011] In the formula, E is the electric field strength of the material, V is the electric potential, ▽ is the Hamiltonian operator, J is the current density vector, T is the temperature, and σ is the electrical conductivity of the material;

[0012] For a superconductor, its non-linear electrical conductivity σ y is derived by the E-J power law as:

[0013]

[0014] In the formula, E C represents the critical electric field, σ y represents the electrical conductivity of the superconducting layer, J c (T) represents the critical current density at temperature T, and n represents the first material parameter;

[0015] The temperature dependence of the electrical conductivity of the superconducting layer is represented by the temperature dependence of its critical current J C as:

[0016]

[0017] In the formula, J CO is the critical current at the operating temperature, T C is the critical temperature, T 0 is the initial temperature, and β is the second material constant.

[0018] Furthermore, in the electrical module, current shunting is achieved in the following manner:

[0019] At the initial moment, the current only flows in the superconducting layer. When the tape undergoes flux decay, the superconducting layer returns to a resistive state, and the current is shunted to the copper layer and the NI substrate. Based on the difference in the current density fluxes on the upper and lower surfaces of the superconducting layer, the driving current is shunted to the copper layer and the NI substrate.

[0020] Furthermore, the difference in the current density fluxes on the upper and lower surfaces of the superconducting layer is determined in the following manner:

[0021] Obtained from the control equation of the electric field:

[0022] J = σE = -σ▽V

[0023] For the superconducting layer, assuming that the electric potential V varies uniformly along the thickness, then:

[0024]

[0025] In the formula, d is the material thickness, V + is the electric potential of the upper surface, V - is the electric potential of the lower surface;

[0026] The current density fluxes on the upper and lower surfaces of the superconducting layer are obtained as:

[0027]

[0028] In the formula, is the current density flux on the upper surface of the superconducting layer, is the current density flux on the lower surface of the superconducting layer; d y is the thickness of the superconducting layer; are the electric potentials on the upper and lower surfaces of the superconducting layer; n + is the outer normal vector of the upper surface of the superconducting layer, and n - is the outer normal vector of the lower surface of the superconducting layer;

[0029] According to the vertical position relationship of the materials and the interface continuity, by using the current density flux on the lower surface of the silver layer to replace the current density flux on the upper surface of the superconducting layer, and using the current density flux on the upper surface of the buffer layer to replace the current density flux on the lower surface of the superconducting layer, we have:

[0030]

[0031] In the formula, σ S and σ b are the conductivities of the silver layer and the buffer layer respectively; d S and d b are the thicknesses of the silver layer and the buffer layer respectively; is the electric potential on the upper and lower surfaces of the silver layer; is the electric potential on the upper and lower surfaces of the buffer layer; is the current density flux on the lower surface of the silver layer, is the current density flux on the upper surface of the buffer layer;

[0032] According to the vertical position relationship of the materials and the interface continuity, by using the electric potential on the lower surface of the upper copper layer to replace the electric potential on the upper surface of the silver layer, the electric potential on the upper surface of the superconducting layer to replace the electric potential on the lower surface of the silver layer, the electric potential on the lower surface of the superconducting layer to replace the electric potential on the upper surface of the buffer layer, and the electric potential on the upper surface of the NI substrate to replace the electric potential on the lower surface of the buffer layer, we have:

[0033]

[0034] In the formula, is the electric potential on the lower surface of the upper copper layer, is the electric potential on the upper surface of the superconducting layer, is the electric potential on the lower surface of the superconducting layer, is the electric potential on the upper surface of the NI substrate;

[0035] Then, the difference between the current density fluxes on the upper and lower surfaces of the superconducting layer is:

[0036]

[0037] Wherein, ΔJ represents the difference in the current density flux between the upper surface and the lower surface of the superconducting layer.

[0038] Further, in the electrical module, the current flowing from the superconducting layer to the copper layer and the NI substrate is hindered by the silver layer and the buffer layer. The process of obtaining the expression of the interlayer contact resistance by using the weak contribution to represent the influence of the thin layer contact resistance through the weak form method includes:

[0039] Determine the current conservation equation, expressed as:

[0040]

[0041] Separate the term in the Z direction from the current conservation equation:

[0042]

[0043] Wherein, ▽ t represents the Hamiltonian operator containing only the planar direction, represents the partial differential symbol, E Z represents the electric field in the Z direction, J Z represents the current density in the Z direction, and z represents the direction perpendicular to the thickness of the strip;

[0044] In the case where the electrical parameters are constant in the Z direction, the term in the Z direction separated from the current conservation equation is integrated along the Z direction, and we get:

[0045]

[0046] Wherein, represents the average temperature, represents the average electric potential, represents the opposite of the difference in the current density flux between the upper surface and the lower surface of the superconducting layer, represents the planar remainder, d y is the thickness of the superconducting layer, is the conductivity of the superconducting layer at the average temperature;

[0047] According to the continuity of the current and the electric potential, we get:

[0048]

[0049] Wherein

[0050] Further, the heat transfer between multiple layers is hindered by the silver layer and the buffer layer. The process of obtaining the expression of the interlayer contact thermal resistance by using the weak contribution to represent the influence of the thin layer contact thermal resistance through the weak form method is as follows:

[0051] Considering only the influence of the contact thermal resistance between the silver layer and the buffer layer, the weak form of the classical Fourier heat conduction equation is derived and expressed as:

[0052]

[0053] where ρ is the material density, C is the material specific heat, K is the material thermal conductivity, Q is the Joule heat, ▽ is the Hamiltonian operator, T is the temperature, and t is the time;

[0054] For the superconducting layer, the terms in the z - direction of the heat conduction equation are separated to obtain:

[0055]

[0056] where ρ y (T) is the density of the superconducting layer at temperature T, C y (T) is the specific heat of the superconducting layer at temperature T, ▽ t is the Hamiltonian operator containing only the planar direction, z represents the direction perpendicular to the tape thickness, K y (T) is the heat transfer coefficient of the superconducting layer at temperature T, and Q(T) is the Joule heat at temperature T;

[0057] In the case where the thermal parameters are constant along the z - direction, the separated term in the z - direction of the heat conduction equation is integrated over the layer thickness to obtain:

[0058]

[0059] where d y is the thickness of the superconducting layer, is the average temperature, is the density of the superconducting layer at the average temperature , is the specific heat of the superconducting layer at the average temperature , is the heat transfer coefficient of the superconducting layer at the average temperature , is the Joule heat at the average temperature ;

[0060] where:

[0061]

[0062] where F + , F - are the heat fluxes on the upper and lower surfaces of the superconducting layer, respectively; is the temperature of the lower surface of the upper copper layer; is the temperature of the upper surface of the NI substrate; are the temperatures of the upper and lower surfaces of the superconducting layer; d S and d bare the thicknesses of the silver layer and the buffer layer, respectively; K S and K b are the heat transfer coefficients of the silver layer and the buffer layer, respectively.

[0063] Furthermore, in the thermal module, a non-classical Fourier heat conduction equation based on the generalized thermoelasticity principle is adopted, expressed as:

[0064]

[0065] In the formula, t 0 is the thermal relaxation time, λ and μ are the Lame coefficients of the material, α is the coefficient of thermal expansion, u, v, and w are the displacements of the material in the x, y, and z directions, Q J is the Joule heat when the current density is J, T 0 is the initial temperature, x, y, and z are the coordinate components respectively, k is the heat transfer coefficient, ρ is the density, and c is the specific heat.

[0066] Furthermore, the mechanical module is constructed in the following manner:

[0067] When each layer of the strip is a linear elastic material and the linear elastic material has a thermal expansion effect, the mechanical parameters satisfy the equilibrium equation, the geometric equation, the physical equation, and the thermal expansion equation;

[0068] The equilibrium equation is expressed as:

[0069]

[0070] In the formula, σ x is the normal stress component in the x direction, σ y is the normal stress component in the y direction, σ z is the normal stress component in the z direction, τ xy is the shear stress component in the xy direction, τ xz is the shear stress component in the xz direction, τ yz is the shear stress component in the yz direction, f x is the body force in the x direction, f y is the body force in the y direction, f z is the body force in the z direction;

[0071] The geometric equation is expressed as:

[0072]

[0073] In the formula, ε x is the normal strain in the x direction, ε y is the normal strain in the y direction, ε z is the normal strain in the z direction, γ xy is the shear strain in the xy direction, γ xz is the shear strain in the xz direction, γyz is the shear strain in the yz direction;

[0074] The physical equation is expressed as:

[0075]

[0076] In the formula, E1 is the elastic modulus and G is the shear modulus;

[0077] The thermal expansion equation is expressed as:

[0078] ε t = α(T - T 0 )

[0079] In the formula, ε t is the thermal strain of the material, α is the thermal expansion coefficient, T 0 is the initial temperature, and T is the temperature.

[0080] In a second aspect, the present invention provides a quench characterization device for multi-field coupling of high-temperature superconducting coated conductors, and the device includes:

[0081] Establish a coupled force-electric-thermal multi-physics field model; wherein, the coupled force-electric-thermal multi-physics field model includes an electrical module, a mechanical module, and a thermal module;

[0082] In the electrical module and the thermal module, the material conductivity is a function of temperature, and the joule heat causes temperature changes, thereby realizing bi-directional electro-thermal coupling;

[0083] In the thermal module and the mechanical module, the temperature causes thermal strain in the tape, and there is a strain term in the non-classical Fourier heat conduction equation, realizing bi-directional force-thermal coupling.

[0084] In a third aspect, the present invention provides a readable storage medium storing one or more programs, and the one or more programs can be executed by one or more processors to implement the method as described above.

[0085] The present invention has at least the following beneficial effects:

[0086] 1. A model for representing the interlayer contact resistance and thermal resistance through weak contributions is established, eliminating the need to establish thin layers, and greatly reducing the computational complexity when considering the electro-thermal effects of thin layers.

[0087] 2. The further promotion of the generalized thermoelastic principle in high-temperature superconducting tapes is realized, making the numerical simulation process more consistent with the quench process of high-temperature superconducting tapes.

[0088] 3. A method for representing the quench characteristics of high-temperature superconducting coated conductors under the condition of coupled force-electric-thermal multi-physics fields is established. Description of the Drawings

[0089] Figure 1 Shows a cross-sectional view of a high-temperature superconducting tape according to an embodiment of the present invention;

[0090] Figure 2 Shows a schematic diagram of the lamination of the tape according to an embodiment of the present invention;

[0091] Figure 3 Shows a schematic diagram of applying a heat pulse to the upper copper layer according to an embodiment of the present invention;

[0092] Figure 4 Shows a front view of the tape model according to an embodiment of the present invention;

[0093] Figure 5 Shows a cross-sectional view of the tape model according to an embodiment of the present invention;

[0094] Figure 6 Shows a schematic diagram of the superconducting layer according to an embodiment of the present invention;

[0095] Figure 7 Shows a boundary numbering diagram according to an embodiment of the present invention;

[0096] Figure 8 Shows a schematic diagram of multi-field coupling according to an embodiment of the present invention;

[0097] Figure 9 Shows a structural diagram of a quench characterization device for multi-field coupling of a high-temperature superconducting coated conductor according to an embodiment of the present invention.

[0098] Reference numerals:

[0099] 101 - upper copper layer; 102 - silver layer; 103 - superconducting layer; 104 - buffer layer; 105 - NI substrate; 106 - lower copper layer; 901 - processor. Detailed implementation manners

[0100] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners. The embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings and specific examples, but shall not be construed as limiting the present invention. For the steps described herein, if there is no necessity for a front-back relationship between them, the order in which they are described as examples herein shall not be regarded as a limitation, and those skilled in the art should know that they can be adjusted in order as long as the logic between them is not destroyed and the entire process cannot be realized.

[0101] High-temperature superconducting tapes have attracted much attention due to their good current-carrying capacity. In recent years, with the improvement of the preparation process, the electrical and mechanical properties of superconducting tapes have been significantly enhanced. However, there are often defects inside the commercially produced high-temperature superconducting tapes, so that thermal disturbances are easily induced during operation, resulting in the quench of the tapes. The slow quench propagation speed (NZPV) makes it particularly difficult to detect in a timely manner. The traditional quench detection methods based on voltage and temperature are not sufficient, and the tapes often suffer mechanical damage and burnout before the quench is detected. Therefore, it is necessary to develop a new strain-based quench detection method. Thus, it is still necessary to study the mechanical response induced by the quench of the tapes, explore the reflection of mechanical deformation on the quench of the tapes, and try to prove the theoretical feasibility of the strain-based quench detection scheme.

[0102] Based on this, an embodiment of the present invention provides a quench characterization method for multi-field coupling of high-temperature superconducting coated conductors. As Figure 1 and Figure 2 shown, Figures 4 and 5 are respectively a cross-sectional view of the high-temperature superconducting tape and a schematic diagram of the tape lamination applied to this method. It includes an upper copper layer 101, a silver layer 102, a superconducting layer 103, a buffer layer 104, a NI substrate 105, and a lower copper layer 106 arranged in sequence from top to bottom. In the superconducting state, all the current flows in the superconducting layer 103 and no current passes through other layers. When a thermal disturbance occurs, the local temperature of the tape rises above its critical temperature (92K), resulting in local quench. The current in this area will shunt from the superconducting layer 103 to the copper layer (including the upper copper layer 101 and the lower copper layer 106), thereby generating joule heat. Heat conduction will cause subsequent quenches in other areas, that is, the propagation of the quench. In this process, the electro-thermal-mechanical multi-fields of the high-temperature superconducting tape are coupled with each other. The interlayer contact resistance and thermal resistance are crucial for interlayer shunting and heat conduction. In this embodiment, the weak contribution is used to represent the interlayer contact resistance and thermal resistance, successfully regulating the current shunting and interlayer heat transfer. And a mixed-dimensional modeling method is adopted. The superconducting layer 103 is represented by a two-dimensional plane, ignoring the silver layer 102 and the buffer layer 104 and only considering the influence of their contact resistance and thermal resistance, which not only avoids meshing them but also improves the calculation efficiency and realizes the regulation of interlayer current shunting. Moreover, considering the slow quench propagation speed (heat propagation speed) of high-temperature superconductors and the non-negligible strain generated during the quench process of superconducting materials, this embodiment adopts a non-classical heat conduction equation based on the generalized thermoelasticity principle, including a strain energy term and a thermal relaxation time term, considering the finiteness of temperature propagation and the influence of strain on the quench.

[0103] In this embodiment, through the finite element simulation of the quench of the high-temperature superconducting tape, the variation laws of multiple physical quantities during the quench process are characterized, and the sensitivity of multiple physical quantities to the quench is compared, preliminarily proving the theoretical feasibility of the strain-based quench detection scheme.

[0104] In this embodiment, the method realizes representing the interlayer contact resistance and thermal resistance with weak contributions, successfully achieves current shunting, and adds the volume strain term and thermal relaxation time term by using the generalized thermoelastic principle to characterize the variation characteristics of multiple physical quantities during the quench process of high-temperature superconducting coated conductors by establishing a finite element model for the quench of hybrid-dimensional high-temperature superconducting tapes.

[0105] Specifically, the method includes the following steps: establishing a coupled multi-physics model of force, electricity, and heat; wherein, the coupled multi-physics model of force, electricity, and heat includes an electrical module, a mechanical module, and a thermal module; in the electrical module and the thermal module, the material conductivity is a function of temperature, and the joule heat causes temperature changes, thereby realizing the two-way coupling of electricity and heat; in the thermal module and the mechanical module, the temperature causes thermal strain in the tape, and there is a strain term in the non-classical Fourier heat conduction equation, realizing the two-way coupling of force and heat.

[0106] Next, the construction methods and action principles of the three modules of the electrical module, the mechanical module, and the thermal module will be described in detail.

[0107] First, for the electrical module, the basic equation of the electrical module is determined in the following way:

[0108] In view of the high aspect ratio of the tape and the existence of thin layers, in this embodiment, only the copper layer and the NI substrate are modeled as three-dimensional, the superconducting layer is a two-dimensional thin shell, the silver layer and the buffer layer are not modeled, and only their contact resistance effects are considered. The electric field control method used in this embodiment is method. The method is a method of solving Maxwell's equations by taking only the electric potential as a variable, which can effectively improve the speed and accuracy of the simulation process. The control equation of the

[0109]

[0110] method based on Ampere's law and the current conservation equation is:

[0111] When modeling, the method is used as the control equation. Since NZPV is slow, by removing the time derivative term of the magnetic potential, the slowly changing magnetic field is ignored, so that the magnetic potential and the electric potential in Maxwell's equation are decoupled. This can improve the speed of model calculation and reduce the complexity of model setup.

[0112] For the superconductor, the conductivity σ y of the superconducting layer is derived by the E-J power law as:

[0113]

[0114] In the formula, E C represents the critical electric field, and σ y represents the conductivity of the superconducting layer; J C (T) represents the critical current density, and n represents the first material parameter.

[0115] Among them, the critical electric field E C = 1×10 -4 V / m, and the temperature dependence of the conductivity σ of the superconducting layer is represented by the temperature dependence of the critical current J y : C In the formula, J

[0116]

[0117] is the critical current at the working temperature, T CO is the critical temperature, T C is the initial temperature, and β is the second material constant. 0 In the electrical module, current shunting is achieved in the following manner:

[0118] At the initial moment, the current only flows in the superconducting layer. When the tape undergoes a quench, the superconducting layer returns to a resistive state, and the current is shunted to the copper layer and the NI substrate. To drive the current to be shunted to the copper layer and the NI substrate, the difference in the current density fluxes on the upper and lower surfaces of the superconducting layer is given in this embodiment. According to

[0119] the control equation of the method, the expression of the current density is obtained as: For a thin layer, in this embodiment, the electric potential V can be regarded as uniformly varying along the thickness, and then the expression of the current density is further determined as:

[0120] J = σE = -σ▽V

[0121]

[0122]

[0123] In the formula, d is the material thickness, V + is the electric potential on the upper surface, V - is the electric potential on the lower surface, and σ is the material conductivity. y

[0124] According to the expression of the current density, the current density fluxes on the upper and lower surfaces of the superconducting layer can be obtained as:

[0125]

[0126] In the formula, is the current density flux on the upper surface of the superconducting layer, is the current density flux on the lower surface of the superconducting layer; d y is the thickness of the superconducting layer; are the electric potentials of the upper and lower surfaces of the superconducting layer; n + is the outer normal vector of the upper surface of the superconducting layer, n - is the outer normal vector of the lower surface of the superconducting layer.

[0127] Due to the continuity of the interface current, in this embodiment, the current density flux of the lower surface of the silver layer is used to replace the current density flux of the upper surface of the superconducting layer, and the current density flux of the upper surface of the buffer layer is used to replace the current density flux of the lower surface of the superconducting layer.

[0128]

[0129] In the formula, σ S and σ b are the conductivities of the silver layer and the buffer layer respectively; d S and d b are the thicknesses of the silver layer and the buffer layer respectively; are the electric potentials of the upper and lower surfaces of the silver layer; are the electric potentials of the upper and lower surfaces of the buffer layer; is the current density flux of the lower surface of the silver layer, is the current density flux of the upper surface of the buffer layer.

[0130] According to the continuity of the electric potential, that is, from the position relationship between the upper and lower layers of the material and the interface continuity, in this embodiment, the electric potential of the lower surface of the upper copper layer is used to replace the electric potential of the upper surface of the silver layer, the electric potential of the upper surface of the superconducting layer is used to replace the electric potential of the lower surface of the silver layer, the electric potential of the lower surface of the superconducting layer is used to replace the electric potential of the upper surface of the buffer layer, and the electric potential of the upper surface of the NI substrate is used to replace the electric potential of the lower surface of the buffer layer. The electric potential of the upper surface of the NI substrate replaces to obtain:

[0131]

[0132] In the formula, is the electric potential of the lower surface of the upper copper layer, is the electric potential of the upper surface of the superconducting layer, is the electric potential of the lower surface of the superconducting layer, is the electric potential of the upper surface of the NI substrate.

[0133] Then the difference between the current density fluxes of the upper and lower surfaces of the superconducting layer is:

[0134]

[0135] In the formula, ΔJ represents the difference between the current density fluxes of the upper and lower surfaces of the superconducting layer.

[0136] In the electrical module, the flow of current from the superconducting layer to the copper layer and the NI substrate is hindered by the silver layer and the buffer layer, i.e., affected by the interlayer contact resistance. To simplify the program and improve the calculation efficiency, this embodiment uses a weak contribution to represent the influence of the thin layer contact resistance, and obtains the interlayer contact resistance expression (two-dimensional tangential electric equation) through the weak form method. Here, the contact resistance equation required for using the weak contribution is derived from the weak form equation. First, there is the current conservation equation:

[0137] ▽·σ y ▽V=0

[0138] Separate the terms in the Z direction:

[0139]

[0140] Where ▽ t represents the Hamiltonian operator containing only the planar direction, represents the partial differential symbol, E Z represents the electric field in the Z direction, J Z represents the current density in the Z direction, and z represents the direction perpendicular to the thickness of the strip.

[0141] Given that the superconducting layer is a thin layer, assuming that the electrical parameters are constant in the Z direction (thickness direction), i.e., across the thickness of the superconducting layer, integrating this equation in the Z direction gives:

[0142]

[0143] Where represents the average temperature, represents the average electric potential, represents the opposite of the difference in the current density fluxes on the upper and lower surfaces of the superconducting layer, represents the planar remainder, d y is the thickness of the superconducting layer, is the electrical conductivity of the superconducting layer at the average temperature.

[0144] According to the continuity of current and electric potential, there is also:

[0145]

[0146] Where The two terms on the right side are the boundary condition equations of the interlayer contact resistance derived by the weak form method, which will be represented by a weak contribution and can also be understood as the difference in the current density fluxes on the upper and lower surfaces of the superconducting layer. Note that the test function term is omitted in this embodiment.

[0147] Secondly, for the thermal module, only consider the influence of the contact thermal resistance between the silver layer and the buffer layer. This embodiment first derives the weak form of the classical Fourier heat conduction equation, expressed as:

[0148]

[0149] Where ρ is the material density, C is the specific heat of the material, K is the thermal conductivity of the material, and all are functions of temperature; Q is the Joule heat, ▽ is the Hamiltonian operator, T is the temperature, and t is the time.

[0150] For the YBCO superconducting layer, in this embodiment, the term in the z-direction of the heat conduction equation is separated to obtain:

[0151]

[0152] In the formula, ρ y (T) is the density of the superconducting layer at temperature T, C y (T) is the specific heat of the superconducting layer at temperature T, ▽ t is the Hamiltonian operator only including the planar direction, z represents the direction perpendicular to the thickness of the tape, K y (T) is the heat transfer coefficient of the superconducting layer at temperature T, and Q(T) is the Joule heat at temperature T.

[0153] Also assume that the thermal parameters are constant along the z-direction, that is, across the thickness of the superconducting layer. Integrate the above formula with respect to the layer thickness to obtain:

[0154]

[0155] In the formula, d y is the thickness of the superconducting layer, is the average temperature, is the average temperature of the superconducting layer density, is the average temperature of the specific heat of the superconducting layer, is the average temperature of the heat transfer coefficient of the superconducting layer, is the average temperature of the Joule heat.

[0156] The last term on the left side of the above formula is approximately the difference in the normal heat fluxes on the upper and lower surfaces of the superconducting layer, and can be written as:

[0157]

[0158] In the formula, F + 、F - are the heat fluxes on the upper and lower surfaces of the superconducting layer respectively; is the temperature of the lower surface of the upper copper layer, which is the temperature of the upper surface of the silver layer by continuity; is the temperature of the upper surface of the NI substrate, which is the temperature of the lower surface of the buffer layer; are the temperatures of the upper and lower surfaces of the superconducting layer; K S is the heat transfer coefficient of the silver layer and Kb are the heat transfer coefficients of the buffer layer respectively. This is the contact thermal resistance boundary condition equation derived by the weak form method, which will be expressed by the weak contribution and can also be understood as the difference in heat fluxes on the upper and lower surfaces of the superconducting layer. Note that the trial function term is omitted here.

[0159] In some embodiments, considering that the temperature propagation speed obtained from the classical Fourier heat conduction law is infinite, on the one hand, this does not conform to the actual situation, and on the other hand, the slow quench propagation speed of high-temperature superconductors will cause a large error between the simulation results using the traditional Fourier heat conduction law and the experiment, which needs to be avoided and improved. Moreover, non-negligible thermal strain will be generated during the quench process of high-temperature superconductors. Therefore, this embodiment adopts the generalized thermoelasticity theory based on the non-classical Fourier heat conduction law, and its heat conduction equation is changed to:

[0160]

[0161] where t 0 is the heat relaxation time, which can be understood as the time required for the temperature (heat) to reach a steady state, λ and μ are the Lame coefficients of the material, α is the coefficient of thermal expansion, u, v, and w are the displacements of the material in the x-direction, y-direction, and z-direction, Q J is the Joule heat, k is the heat transfer coefficient, ρ is the density, and c is the specific heat.

[0162] Compared with the classical Fourier heat conduction equation, this equation has four more terms:

[0163]

[0164] The above four terms include the volumetric strain and the heat relaxation time, which transform the classical Fourier heat conduction equation into a non-classical Fourier heat conduction equation.

[0165] To trigger a quench, as Figure 3 shown, a heat pulse is applied at the end of the copper layer of the tape at a length of 1 / 50. Figure 3 In, x, y, and z represent the length direction, width direction, and thickness direction of the tape.

[0166] Finally, for the mechanical module, when all layers of the tape are linearly elastic materials and the linearly elastic materials have a thermal expansion effect, the mechanical parameters satisfy the equilibrium equation, geometric equation, physical equation, and thermal expansion equation;

[0167] The equilibrium equation is expressed as:

[0168]

[0169] In the formula, σ x is the normal stress in the x-direction, σ y is the normal stress in the y-direction, σ zis the normal stress in the z direction, τ xy is the shear stress in the xy direction, τ xz is the shear stress in the xz direction, τ yz is the shear stress in the yz direction, f x is the body force in the x direction, f y is the body force in the y direction, f z is the body force in the z direction;

[0170] The geometric equations are expressed as:

[0171]

[0172] where ε x is the linear strain in the x direction, ε y is the linear strain in the y direction, ε z is the linear strain in the z direction, u, v, and w are the displacements of the material in the x, y, and z directions, respectively, and γ xy is the shear strain in the xy direction, γ xz is the shear strain in the xz direction, γ yz is the shear strain in the yz direction;

[0173] The physical equations are expressed as:

[0174]

[0175] where E1 is the elastic modulus and G is the shear modulus;

[0176] The thermal expansion equations are expressed as:

[0177] ε t = α(T - T 0 )

[0178] where ε t is the thermal strain of the material, α is the coefficient of thermal expansion, T 0 is the initial temperature, and T is the temperature.

[0179] Next, the embodiments of the present invention will further verify the feasibility of the method proposed by the present invention in combination with a specific example.

[0180] Due to the strong symmetry of the high-temperature superconducting tape model, a 1 / 4 model is selected for modeling in this embodiment, which can reduce the computational complexity. As Figure 4 and Figure 5 shown, the front view and cross-sectional view of the tape model constructed in this embodiment are presented, respectively.

[0181] The silver layer, superconducting layer, and buffer layer are extremely thin compared to other layers. Therefore, in this embodiment, only the copper layer and the NI substrate are modeled as three-dimensional structures, the superconducting layer is simplified to a two-dimensional surface, and the silver layer and buffer layer are ignored, which not only avoids meshing the thin layers but also improves the calculation efficiency.

[0182] In this embodiment, the lower surface of the upper copper layer is selected as the superconducting layer, as Figure 6 shown. The set boundary conditions are as Figure 7 shown, Figure 7 where the markings 1 to 8 in represent the boundary numbers respectively. The boundary conditions include electrical boundary conditions and thermal boundary conditions, as shown in Table 1 and Table 2 respectively.

[0183] Table 1 Electrical Boundary Conditions

[0184]

[0185] Table 2 Thermal Boundary Conditions

[0186]

[0187] In this embodiment, the lower surface of the strip is set as a fixed edge.

[0188] As Figure 8 shown, it is a schematic diagram of multi-field coupling. The electrical conductivity σ of the material is a function of temperature T, and the Joule heat Q J will cause temperature changes, realizing electro-thermal bidirectional coupling; temperature will cause thermal strain in the strip, and there is a strain term in the non-classical Fourier heat conduction equation, realizing force-thermal bidirectional coupling.

[0189] The embodiment of the present invention also provides a quench characterization device for multi-field coupling of high-temperature superconducting coated conductors, as Figure 9 shown. The device includes a processor 901, and the processor 901 is configured to:

[0190] Establish a coupled multi-physics field model of force, electricity, and heat; wherein, the coupled multi-physics field model of force, electricity, and heat includes an electrical module, a mechanical module, and a thermal module;

[0191] In the electrical module and the thermal module, the electrical conductivity of the material is a function of temperature, and the Joule heat causes temperature changes, thereby realizing electro-thermal bidirectional coupling;

[0192] In the thermal module and the mechanical module, temperature causes thermal strain in the strip, and there is a strain term in the non-classical Fourier heat conduction equation, realizing force-thermal bidirectional coupling.

[0193] In some embodiments, the processor 901 is further configured to establish the electrical module by the following method:

[0194] The copper layer and the NI substrate are modeled three-dimensionally, and the superconducting layer is modeled as a two-dimensional thin shell. Geometrically, the silver layer and the buffer layer are ignored, and only their contact resistance effects are considered electrically. The three-dimensional control equation for the electric field is determined as follows:

[0195]

[0196] In the formula, E is the electric field strength, V is the electric potential, ▽ is the Hamiltonian operator, J is the current density, T is the temperature, and σ is the electrical conductivity of the material;

[0197] For the superconductor, its non-linear electrical conductivity σ y is derived using the E-J power law as:

[0198]

[0199] In the formula, E C represents the critical electric field, σ y represents the electrical conductivity of the superconducting layer, J c (T) represents the critical current density at temperature T, and n represents the first material parameter;

[0200] The temperature dependence of the electrical conductivity of the superconducting layer is represented by the temperature dependence of the critical current J C as:

[0201]

[0202] In the formula, J CO is the critical current at the operating temperature, T C is the critical temperature, T 0 is the initial temperature, and β is the second material constant.

[0203] In some embodiments, the processor 901 is further configured to achieve current shunting in the electrical module in the following manner:

[0204] At the initial moment, the current only flows in the superconducting layer. When the tape experiences a quench, the superconducting layer returns to a resistive state, and the current is shunted to the copper layer and the NI substrate. Based on the difference in the current density fluxes on the upper and lower surfaces of the superconducting layer, the current is driven to be shunted to the copper layer and the NI substrate.

[0205] In some embodiments, the processor 901 is further configured to determine the difference in the current density fluxes on the upper and lower surfaces of the superconducting layer in the following manner:

[0206] According to the control equation of the electric field, it is obtained that:

[0207] J = σE = -σ▽V

[0208] For the superconducting layer, assuming that the electric potential V varies uniformly along the thickness, then there is:

[0209]

[0210] where d is the material thickness, V + is the potential of the upper surface, V - is the potential of the lower surface, and σ is the material conductivity;

[0211] The current density fluxes on the upper and lower surfaces of the superconducting layer are obtained as:

[0212]

[0213] where is the current density flux on the upper surface of the superconducting layer, is the current density flux on the lower surface of the superconducting layer; d y is the thickness of the superconducting layer; are the potentials on the upper and lower surfaces of the superconducting layer; n + is the outer normal vector of the upper surface, n - is the outer normal vector of the lower surface;

[0214] From the position relationship between the upper and lower layers of the material and the interface continuity, using the current density flux on the lower surface of the silver layer to replace the current density flux on the upper surface of the superconducting layer, and using the current density flux on the upper surface of the buffer layer to replace the current density flux on the lower surface of the superconducting layer, there is:

[0215]

[0216] where σ S and σ b are the conductivities of the silver layer and the buffer layer respectively; d S and d b are the thicknesses of the silver layer and the buffer layer respectively; are the potentials on the upper and lower surfaces of the silver layer; are the potentials on the upper and lower surfaces of the buffer layer; is the current density flux on the lower surface of the silver layer, is the current density flux on the upper surface of the buffer layer;

[0217] From the position relationship between the upper and lower layers of the material and the interface continuity, using the potential on the lower surface of the upper copper layer to replace the potential on the upper surface of the silver layer, the potential on the upper surface of the superconducting layer to replace the potential on the lower surface of the silver layer, the potential on the lower surface of the superconducting layer to replace the potential on the upper surface of the buffer layer, and the potential on the upper surface of the NI substrate to replace the potential on the lower surface of the buffer layer, there is:

[0218]

[0219] where is the potential on the lower surface of the upper copper layer, is the potential on the upper surface of the superconducting layer, is the potential on the lower surface of the superconducting layer, is the surface potential of the NI substrate;

[0220] Then the difference in the current density flux between the upper and lower surfaces of the superconducting layer is:

[0221]

[0222] In the formula, ΔJ represents the difference in the current density flux between the upper surface and the lower surface of the superconducting layer.

[0223] In some embodiments, the processor 901 is further configured to, in the electrical module, when the current flows from the superconducting layer to the copper layer and the NI substrate and is blocked by the silver layer and the buffer layer, represent the influence of the thin-film contact resistance with a weak contribution, and the process of obtaining the expression of the interlayer contact resistance by the weak form method includes:

[0224] Determine the current conservation equation, expressed as:

[0225]

[0226] Separate the term in the Z direction from the current conservation equation:

[0227]

[0228] In the formula, ▽ t represents the Hamiltonian operator containing only the planar direction, represents the partial differential symbol, E Z represents the electric field in the Z direction, J Z represents the current density in the Z direction, and z represents the direction perpendicular to the thickness of the strip;

[0229] In the case where the electrical parameters are constant in the Z direction, then integrate the term in the Z direction separated from the current conservation equation along the Z direction, and obtain:

[0230]

[0231] In the formula, represents the average temperature, represents the average electric potential, represents the opposite of the difference in the current density flux between the upper surface and the lower surface of the superconducting layer, represents the planar remainder, d y is the thickness of the superconducting layer, is the conductivity of the superconducting layer at the average temperature;

[0232] According to the continuity of current and electric potential, obtain:

[0233]

[0234] where

[0235] In some embodiments, the processor 901 is further configured to represent the influence of the thin-layer contact thermal resistance by weak contribution. The process of obtaining the expression of the interlayer contact thermal resistance by the weak form method is as follows:

[0236] When only considering the influence of the contact thermal resistance between the silver layer and the buffer layer, the weak form of the classical Fourier heat conduction equation is derived and expressed as:

[0237]

[0238] In the formula, ρ is the material density, C is the specific heat of the material, K is the thermal conductivity of the material, Q is the Joule heat, ▽ is the Hamiltonian operator, T is the temperature, and t is the time;

[0239] For the superconducting layer, the term in the z direction of the heat conduction equation is separated to obtain:

[0240]

[0241] In the formula, ρ y (T) is the density of the superconducting layer at temperature T, C y (T) is the specific heat of the superconducting layer at temperature T, ▽ t is the Hamiltonian operator only including the planar direction, z represents the direction perpendicular to the thickness of the strip, K y (T) is the heat transfer coefficient of the superconducting layer at temperature T, and Q(T) is the Joule heat at temperature T;

[0242] When the thermal parameters are constant along the z direction, the separated term in the z direction of the heat conduction equation is integrated with respect to the layer thickness to obtain:

[0243]

[0244] In the formula, d y is the thickness of the superconducting layer, is the average temperature, is the average temperature of the superconducting layer density, is the average temperature of the superconducting layer specific heat, is the average temperature of the superconducting layer heat transfer coefficient, is the average temperature of the Joule heat;

[0245] Where:

[0246]

[0247] In the formula, F + 、F -are the heat fluxes on the upper and lower surfaces of the superconducting layer, respectively; is the temperature of the lower surface of the upper copper layer; is the temperature of the upper surface of the NI substrate; are the temperatures of the upper and lower surfaces of the superconducting layer; d S and d b are the thicknesses of the silver layer and the buffer layer, respectively; K S and K b are the heat transfer coefficients of the silver layer and the buffer layer, respectively.

[0248] In some embodiments, the processor 901 is further configured to, in the thermal module, adopt a non-classical Fourier heat conduction equation based on the generalized thermoelasticity principle, expressed as:

[0249]

[0250] where t 0 is the thermal relaxation time, λ and μ are the Lame coefficients of the material, α is the coefficient of thermal expansion, u, v, and w are the displacements of the material in the x, y, and z directions, Q J is the Joule heat when the current density is J, T 0 is the initial temperature, x, y, and z are the coordinate components respectively, k is the heat transfer coefficient, ρ is the density, and c is the specific heat.

[0251] In some embodiments, the processor 901 is further configured to construct a mechanical module in the following manner:

[0252] In the case where each layer of the strip is a linear elastic material and the linear elastic material has a thermal expansion effect, the mechanical parameters satisfy the equilibrium equation, the geometric equation, the physical equation, and the thermal expansion equation;

[0253] The equilibrium equation is expressed as:

[0254]

[0255] where σ x is the normal stress component in the x direction, σ y is the normal stress component in the y direction, σ z is the normal stress component in the z direction, τ xy is the shear stress component in the xy direction, τ xz is the shear stress component in the xz direction, τ yz is the shear stress component in the yz direction, f x is the body force in the x direction, f y is the body force in the y direction, f z is the body force in the z direction;

[0256] The geometric equation is expressed as:

[0257]

[0258] In the formula, ε x is the normal strain in the x direction, ε y is the normal strain in the y direction, ε z is the normal strain in the z direction, u, v, and w are the displacements of the material in the x direction, y direction, and z direction, and γ xy is the shear strain in the xy direction, γ xz is the shear strain in the xz direction, γ yz is the shear strain in the yz direction;

[0259] The physical equation is expressed as:

[0260]

[0261] In the formula, E1 is the elastic modulus and G is the shear modulus;

[0262] The thermal expansion equation is expressed as:

[0263] ε t = α(T - T 0 )

[0264] In the formula, ε t is the thermal strain of the material, α is the coefficient of thermal expansion, T 0 is the initial temperature, and T is the temperature.

[0265] It should be noted that the structure of each quench characterization device for multi-field coupling of high-temperature superconducting coated conductors described in this embodiment belongs to the same technical concept as the previously described quench characterization method for multi-field coupling of high-temperature superconducting coated conductors, and achieves the same beneficial effects through the same principle, which will not be elaborated here.

[0266] The embodiment of the present invention also provides a readable storage medium, which stores one or more programs, and the one or more programs can be executed by one or more processors to implement the method described in any of the above embodiments.

[0267] The above description is intended to be illustrative and not restrictive. For example, the above examples (or one or more aspects thereof) may be used in combination with each other. For instance, those of ordinary skill in the art may use other embodiments when reading the above description. Additionally, in the above detailed description, various features may be grouped together to simplify the present invention. This should not be construed as an intention that the features of an unclaimed invention are necessary for any claim. On the contrary, the subject matter of the present invention may be less than all of the features of a particular embodiment of the invention. Thus, the appended claims are incorporated herein by way of example or embodiment, where each claim independently serves as a separate embodiment, and it is contemplated that these embodiments may be combined with each other in various combinations or permutations. The scope of the present invention should be determined with reference to the appended claims and the full scope of equivalents to which those claims are entitled.

Claims

1. A method for characterizing quench of multi-field coupling of a high-temperature superconducting coated conductor, characterized in that: The method comprises: Establishing a mechanical, electrical, and thermal multi-physics field coupling model; wherein the mechanical, electrical, and thermal multi-physics field coupling model includes an electrical module, a mechanical module, and a thermal module; In the electrical module and thermal module, the material conductivity is a function of temperature, and Joule heat causes temperature change, thereby achieving electrical-thermal bidirectional coupling; In the thermal module and the mechanical module, the temperature causes thermal strain in the strip, and the non-classical Fourier heat conduction equation used in the temperature field contains a strain term to achieve bidirectional force-heat coupling.

2. The method for characterizing quench of multi-field coupling of a high-temperature superconducting coated conductor according to claim 1, characterized in that: The electrical module is created as follows: The copper layer and NI substrate are modeled as three-dimensional, the superconducting layer is a two-dimensional thin shell, the silver layer and the buffer layer are geometrically ignored, and only the contact resistance is considered electrically. The three-dimensional control equation of the electric field is determined as: Where E is the electric field strength of the material, V is the electric potential, ▽ is the Hamiltonian operator, J is the current density vector, T is the temperature, and σ is the material conductivity; For superconductors, the nonlinear conductivity σ y Using the EJ power law, it is derived as: In the formula, E C represents the critical electric field, σ y represents the conductivity of the superconducting layer, J c (T) represents the critical current density when the temperature is T, and n represents the first material parameter; The temperature dependence of the conductivity of the superconducting layer is determined by its critical current J C The temperature dependence of is expressed as: In the formula, J CO is the critical current at operating temperature, T C is the critical temperature, T0 is the initial temperature, and β is the second material constant.

3. The method for characterizing quench of multi-field coupling of a high-temperature superconducting coated conductor according to claim 2, characterized in that: In the electrical module, current splitting is achieved in the following manner: At the initial moment, the current only flows in the superconducting layer. When the strip quenches, the superconducting layer returns to a resistive state, and the current is diverted to the copper layer and the NI substrate. Based on the difference in current density flux between the upper and lower surfaces of the superconducting layer, the driving current is diverted to the copper layer and the NI substrate.

4. The method for characterizing quench of multi-field coupling of a high-temperature superconducting coated conductor according to claim 3, characterized in that: The difference in current density flux between the upper and lower surfaces of the superconducting layer is determined as follows: According to the governing equation of the electric field, we get: J=σE=-σ▽V For the superconducting layer, the potential V is considered to vary uniformly along the thickness, then: Where d is the material thickness, V + is the upper surface potential, V - is the lower surface potential; The current density flux on the upper and lower surfaces of the superconducting layer is obtained as: In the formula, is the current density flux on the upper surface of the superconducting layer, is the current density flux on the lower surface of the superconducting layer; d y is the thickness of the superconducting layer; is the upper and lower surface potential of the superconducting layer; n + is the outer normal vector of the superconducting layer surface, n - is the outer normal vector of the lower surface of the superconducting layer; According to the positional relationship between the upper and lower layers of the material and the continuity of the interface, the current density flux on the lower surface of the superconducting layer is replaced by the current density flux on the lower surface of the silver layer, and the current density flux on the upper surface of the buffer layer is replaced by the current density flux on the lower surface of the superconducting layer. Then, we have: In the formula, σ S and σ b are the conductivity of the silver layer and the buffer layer respectively; d S and d b are the thickness of the silver layer and the buffer layer respectively; V s + 、V s - is the upper and lower surface potential of the silver layer; is the upper and lower surface potential of the buffer layer; is the current density flux under the silver layer, is the surface current density flux on the buffer layer; According to the positional relationship between the upper and lower layers of the material and the continuity of the interface, the lower surface potential of the upper copper layer is used to replace the upper surface potential of the silver layer, the upper surface potential of the superconducting layer is used to replace the lower surface potential of the silver layer, the lower surface potential of the superconducting layer is used to replace the upper surface potential of the buffer layer, and the upper surface potential of the NI substrate is used to replace the lower surface potential of the buffer layer. In the formula, is the surface potential of the upper copper layer, is the surface potential of the superconducting layer, is the surface potential under the superconducting layer, is the surface potential on the NI substrate; The difference in current density flux between the upper and lower surfaces of the superconducting layer is: Where ΔJ represents the difference in current density flux between the upper surface of the superconducting layer and the lower surface of the superconducting layer.

5. The method for characterizing quench of multi-field coupling of a high-temperature superconducting coated conductor according to claim 4, characterized in that: In the electrical module, the current flowing from the superconducting layer to the copper layer and the NI substrate is hindered by the silver layer and the buffer layer. The weak contribution is used to represent the influence of the thin layer contact resistance. The process of obtaining the interlayer contact resistance expression by the weak form method includes: Determine the current conservation equation, expressed as: ▽·s y ▽V=0 Isolate the Z-direction term from the current conservation equation: In the formula, ▽ t represents the Hamiltonian operator that only contains the plane direction, Represents the partial differential symbol, E Z represents the electric field in the Z direction, J Z represents the current density in the Z direction, where z represents the direction perpendicular to the strip thickness; When the electrical parameters are constant along the Z direction, the term in the Z direction is separated from the current conservation equation and integrated along the Z direction to obtain: In the formula, represents the average temperature, represents the average potential, It represents the inverse of the difference between the current density flux on the upper surface of the superconducting layer and the current density flux on the lower surface of the superconducting layer. represents the plane remainder, d y is the thickness of the superconducting layer, is the conductivity of the superconducting layer at average temperature; According to the continuity of current and potential, we get: in 6. The method for characterizing quench of multi-field coupling of a high-temperature superconducting coated conductor according to claim 1, characterized in that: The heat propagation between multiple layers is hindered by the silver layer and the buffer layer. The weak contribution is used to represent the influence of the thin layer contact thermal resistance. The process of obtaining the interlayer contact thermal resistance expression through the weak form method is as follows: Considering only the contact thermal resistance of the silver layer and the buffer layer, the weak form of the classical Fourier heat conduction equation is derived and expressed as: Where ρ is the material density, C is the material specific heat, K is the material thermal conductivity, Q is the Joule heat, ▽ is the Hamiltonian operator, T is the temperature, and t is the time; For the superconducting layer, the terms in the Z direction of the heat conduction equation are separated to obtain: In the formula, ρ y (T) is the density of the superconducting layer at temperature T, σ y (T) is the specific heat of the superconducting layer at temperature T, ▽ t is the Hamiltonian operator that only includes the plane direction, z represents the direction perpendicular to the strip thickness, K y (T) is the heat transfer coefficient of the superconducting layer at temperature T, Q(T) is the Joule heat at temperature T; When the thermal parameters are constant along the Z direction, the separation term of the heat conduction equation in the Z direction is integrated with respect to the layer thickness to obtain: Where, d y is the thickness of the superconducting layer, is the average temperature, The average temperature The superconducting layer density under The average temperature The specific heat of the superconducting layer below, The average temperature The heat transfer coefficient of the superconducting layer under The average temperature Joule heat under in: In the formula, F + 、F - are the heat fluxes on the upper and lower surfaces of the superconducting layer, respectively; is the lower surface temperature of the upper copper layer; is the surface temperature of the NI substrate; is the upper and lower surface temperature of the superconducting layer; d S and d b are the thickness of the silver layer and the buffer layer respectively; K S and K b are the heat transfer coefficients of the silver layer and the buffer layer, respectively.

7. The method for characterizing quench of multi-field coupling of a high-temperature superconducting coated conductor according to claim 6, characterized in that: In the thermal module, the non-classical Fourier heat conduction equation based on the generalized thermoelastic principle is adopted, which is expressed as: Where t0 is the thermal relaxation time, λ and μ are the Lame coefficients of the material, α is the thermal expansion coefficient, u, v, w are the displacements of the material in the x, y and z directions, Q J is the Joule heat when the current density is J, T0 is the initial temperature, x, y, z are the coordinate components, k is the heat transfer coefficient, ρ is the density, and c is the specific heat.

8. The method for characterizing quench of multi-field coupling of a high-temperature superconducting coated conductor according to claim 7, characterized in that: The mechanics module is constructed as follows: When all layers of the strip are linear elastic materials and the linear elastic materials have thermal expansion effects, the mechanical parameters satisfy the equilibrium equation, geometric equation, physical equation and thermal expansion equation; The equilibrium equation is expressed as: In the formula, σ x is the normal stress component in the x direction, σ y is the normal stress component in the y direction, σ z is the normal stress component in the z direction, τ xy is the shear stress component in the xy direction, τ xz is the shear stress component in the xz direction, τ yz is the shear stress component in the yz direction, f x is the body force in the x direction, f y is the body force in the y direction, f z is the body force in z direction; The geometric equation is expressed as: In the formula, ε x is the positive strain in the x direction, ε y is the positive strain in the y direction, ε z is the positive strain in the z direction, γ xy is the shear strain in the xy direction, γ xz is the shear strain in the xz direction, γ yz is the shear strain in the yz direction; The physical equation is expressed as: In the formula, E1 is the elastic modulus and G is the shear modulus; The thermal expansion equation is expressed as: ε t =α(T-T0) In the formula, ε t is the thermal strain of the material, α is the thermal expansion coefficient, T0 is the initial temperature, and T is the temperature.

9. A quench characterization device for multi-field coupling of a high-temperature superconducting coated conductor, characterized in that: The apparatus comprises a processor configured to: Establishing a mechanical, electrical, and thermal multi-physics field coupling model; wherein the mechanical, electrical, and thermal multi-physics field coupling model includes an electrical module, a mechanical module, and a thermal module; In the electrical module and thermal module, the material conductivity is a function of temperature, and Joule heat causes temperature change, thereby achieving electrical-thermal bidirectional coupling; In the thermal module and the mechanical module, the temperature causes thermal strain in the strip, and there is a strain term in the non-classical Fourier heat conduction equation, realizing force-heat bidirectional coupling. 10 . A non-transitory computer-readable storage medium storing instructions, which, when executed by a processor, perform the method according to claim 1 .

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