Method and system for determining convective heat transfer coefficient of water-cooled magnet coil

Abstract

Disclosed is a method for determining a convective heat transfer coefficient of a water-cooled magnet coil, comprising: when a current having a predetermined current intensity is introduced into a water-cooled magnet coil, acquiring an actually measured average temperature of the water-cooled magnet coil (S10); in finite element analysis software, simulating introducing the current having the predetermined current intensity into a three-dimensional model of the water-cooled magnet coil, and obtaining, by means of emulation, multiple simulated average temperatures of water-cooled magnet coils corresponding to multiple different wall surface roughnesses (S20); fitting the multiple different wall surface roughnesses and the multiple simulated average temperatures respectively corresponding thereto, and obtaining a fitting function (S30); substituting the actually measured average temperature of the water-cooled magnet coil into the fitting function, to obtain a wall surface roughness corresponding to the actually measured average temperature (S40); substituting the wall surface roughness corresponding to the actually measured average temperature of the water-cooled magnet coil into the finite element analysis software, and obtaining, by means of simulation, a convective heat transfer coefficient of the water-cooled magnet coil (S50). Also disclosed is a system for determining a convective heat transfer coefficient of a water-cooled magnet coil.

Description

Method and system for determining convection heat transfer coefficient of water-cooled magnet coil

[0001] Related applications

[0002] This disclosure claims the benefit of priority to Chinese Patent Application No. 202311551565.4 filed on November 21, 2023 with the State Intellectual Property Office of China, the entire disclosure of which is incorporated herein by reference for all purposes. Technical Field

[0003] The present disclosure relates to the technical field of water-cooled magnets, and more particularly, to a method and system for determining the convective heat transfer coefficient of a water-cooled magnet coil. Background Art

[0004] Water-cooled magnets are a crucial component of the Steady High Magnetic Field Facility (SHMFF). Their high magnetic field intensity and rapid excitation speed have made them a highly sought-after platform for extreme conditions experiments. MIT physicist Francis Bitter first proposed the concept of perforated circular rings, a promising new method for generating higher magnetic fields. These perforated circular conductors were later named Bitter plates. Bitter plates and insulating plates are the two essential elements of a water-cooled magnet coil. As shown in Figure 1, Bitter plate 2 is covered with water-cooling holes and has partitions. Insulating plate 1 and Bitter plate 2 have identical water-cooling holes, but their shape and size are typically a dozen times smaller than those of Bitter plate 2. Bitter plates 2 and insulating plates 1 are stacked in a regular, staggered pattern to form a water-cooled magnet water channel, thereby forming a water-cooled magnet coil. Multiple water-cooled magnet coils are combined to form a water-cooled magnet.

[0005] As the magnetic field strength of water-cooled magnets continues to increase, the operating power also increases, so the thermal stability performance of water-cooled magnet coils has become increasingly prominent. At present, the maximum current passed through some water-cooled magnets is close to 40,000A. Such a high current flowing through the magnet will inevitably generate a large amount of Joule heat. In order to ensure the stable operation of the magnet, the Joule heat generated inside the water-cooled magnet needs to be removed by high-speed, high-pressure deionized cooling water. If the heat is not removed in time, the serious consequence of coil burning will occur. Therefore, in the design of water-cooled magnets, the cooling design of the coil is crucial. The convective heat transfer coefficient of the fluid-solid interface is an indispensable key parameter in the cooling design of water-cooled magnet coils. However, factors such as the shape, position, size, and roughness of the water flow channel in the coil will affect the convective heat transfer coefficient. Therefore, it is very difficult to accurately calculate the analytical solution of the convective heat transfer coefficient.

[0006] At present, the method for determining the convective heat transfer coefficient of water-cooled magnets is mostly based on the empirical formula method. The empirical formula currently used is: h = AV p , where V is the velocity of the water, p is close to 1, and A is a constant. There has been much academic discussion regarding the values ​​of A and p, with most agreeing that p is approximately in the range of 0.8 to 1.0. However, due to the uncertainty of the p value, the heat transfer coefficient derived from a simple empirical formula often deviates significantly from the actual value and cannot accurately describe the heat transfer characteristics of water-cooled magnet coils. Experimental measurement of the convective heat transfer coefficient of water-cooled magnet coils offers relatively high accuracy, but requires the development of specialized, large-scale equipment capable of withstanding high-pressure deionized water, which is expensive.

[0007] In the related art, the patent application document with publication number CN115565745A proposes combining finite element simulation methods to analyze and verify the stability of multiple aspects of electromagnetic and thermal forces in superconducting magnet design. When the superconducting magnet adopts a cooling medium to cool down, the junction between the superconducting magnet and the cooling medium is set as a heat flux boundary. The type of heat flux is convective heat flux, that is, the boundary condition is the known wall heat flux rather than the unknown one.

[0008] Summary of the Invention

[0009] The purpose of the present disclosure is to solve the technical problem of how to improve the accuracy and efficiency of solving the heat transfer coefficient of water-cooled magnets while reducing research and development costs.

[0010] A first aspect of the present disclosure provides a method for determining the convective heat transfer coefficient of a water-cooled magnet coil, the method comprising: obtaining a measured average temperature of the water-cooled magnet coil when a current of a predetermined current intensity is passed through the water-cooled magnet coil; simulating the passage of the current of the predetermined current intensity through a three-dimensional model of the water-cooled magnet coil in finite element analysis software, and setting multiple different wall roughnesses, and obtaining multiple simulated average temperatures of the coil corresponding to the multiple different wall roughnesses through simulation, wherein the measured average temperature of the water-cooled magnet coil is between a minimum value and a maximum value of the multiple simulated average temperatures of the water-cooled magnet coil; fitting the multiple different wall roughnesses and their corresponding multiple simulated average temperatures of the water-cooled magnet coil to obtain a fitting function; substituting the measured average temperature of the water-cooled magnet coil into the fitting function to obtain the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil; substituting the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil into the finite element analysis software, and obtaining the convective heat transfer coefficient of the water-cooled magnet coil through simulation.

[0011] In the above-mentioned first aspect, when a current of a predetermined current intensity is passed through the water-cooled magnet coil, the measured average temperature of the water-cooled magnet coil is obtained, including: applying cooling water of a preset temperature to the water-cooled magnet coil, and measuring a first voltage across the water-cooled magnet coil when a first current is passed through the water-cooled magnet coil when the temperature of the water-cooled magnet coil is equal to the temperature of the cooling water; calculating a first resistance of the water-cooled magnet coil at the preset temperature based on the first current and the first voltage; measuring a second voltage across the water-cooled magnet coil when a second current is passed through the water-cooled magnet coil, wherein the current intensity of the second current is greater than the current intensity of the first current; and calculating the measured average temperature of the water-cooled magnet coil when the second current is passed based on the second current, the second voltage and the first resistance.

[0012] In the above-mentioned first aspect, the calculation of the measured average temperature of the water-cooled magnet coil when the second current is passed based on the second current, the second voltage and the first resistance includes: calculating the second resistance of the water-cooled magnet coil when the second current is passed based on the second current and the second voltage; and calculating the measured average temperature of the water-cooled magnet coil when the second current is passed based on the second resistance and the first resistance.

[0013] In the first aspect above, the measured average temperature of the water-cooled magnet coil when the second current is applied is calculated based on the following formula: R2=R1[1+α(T-10)],

[0014] Wherein: R1 is the first resistor, R2 is the second resistor, U1 is the first voltage, I1 is the first current, U2 is the first voltage, I2 is the first current, α is the resistivity temperature coefficient of the water-cooled magnet coil, and T is the measured average temperature of the water-cooled magnet coil when the second current is passed.

[0015] In the first aspect above, the fitting of multiple different wall roughnesses and their corresponding multiple simulated average temperatures of water-cooled magnet coils to obtain a fitting function includes: using the least squares method to fit multiple different wall roughnesses and their corresponding multiple simulated average temperatures of water-cooled magnet coils to obtain a fitting function, wherein the fitting function satisfies the minimum sum of squared errors of the extracted data.

[0016] In the first aspect above, the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil is substituted into the finite element analysis software, and the convective heat transfer coefficient of the water-cooled magnet coil is obtained through simulation, including: substituting the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil into the wall conditions of the fluid-solid interface, and extracting the heat flux and temperature parameters of the fluid-solid interface; based on the heat flux and temperature parameters of the fluid-solid interface, calculating the average convective heat transfer coefficient of the interface between the water-cooled magnet coil and the fluid domain.

[0017] In the first aspect, the temperature parameters include the wall temperature and the average temperature of the water, and the calculation of the average convective heat transfer coefficient of the interface between the water-cooled magnet coil and the fluid domain based on the heat flux and temperature parameters of the fluid-solid interface includes calculating the average convective heat transfer coefficient based on the following formula: q = h·(T W -T f )

[0018] Where: q represents the heat flux, T W represents the wall temperature, T f represents the average temperature of water, and h represents the average convective heat transfer coefficient.

[0019] In the above-mentioned first aspect, after substituting the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil into the finite element analysis software and obtaining the convective heat transfer coefficient of the water-cooled magnet coil through simulation, the method also includes: calling up the temperature cloud map in the finite element analysis software to obtain the temperature distribution of the water-cooled magnet coil.

[0020] The second aspect of the present disclosure further proposes a system for determining the convective heat transfer coefficient of a water-cooled magnet coil, the system comprising a temperature measurement module, a temperature simulation module, a fitting module, a wall roughness calculation module, and a heat transfer coefficient calculation module. The temperature measurement module is used to obtain the measured average temperature of the water-cooled magnet coil when a current of a predetermined current intensity is passed through the water-cooled magnet coil. The temperature simulation module is used to simulate the passage of a current of the predetermined current intensity through a three-dimensional model of the water-cooled magnet coil in finite element analysis software, and to set a plurality of different wall roughnesses, thereby obtaining a plurality of simulated average temperatures of the water-cooled magnet coil corresponding to the plurality of different wall roughnesses through simulation, wherein the measured average temperature of the water-cooled magnet coil is between the minimum and maximum values ​​of the plurality of simulated average temperatures of the water-cooled magnet coil. The fitting module is used to fit the plurality of different wall roughnesses and the plurality of simulated average temperatures of the water-cooled magnet coil corresponding to each of the respective simulated average temperatures to obtain a fitting function. The wall surface roughness calculation module is configured to substitute the measured average temperature of the water-cooled magnet coil into the fitting function to obtain the wall surface roughness corresponding to the measured average temperature of the water-cooled magnet coil. The heat transfer coefficient calculation module is configured to substitute the wall surface roughness corresponding to the measured average temperature of the water-cooled magnet coil into the finite element analysis software to obtain the convective heat transfer coefficient of the water-cooled magnet coil through simulation.

[0021] 10. The system according to claim 9, wherein the temperature measurement module comprises:

[0022] a temperature setting unit, configured to apply cooling water of a preset temperature to the water-cooled magnet coil, and, when the temperature of the water-cooled magnet coil is equal to the temperature of the cooling water, measure a first voltage across the water-cooled magnet coil when a first current is applied to the water-cooled magnet coil;

[0023] a first resistance calculation unit, configured to calculate a first resistance of the water-cooled magnet coil at the preset temperature according to the first current and the first voltage;

[0024] The current supply unit is configured to measure a second voltage across the water-cooled magnet coil when a second current is supplied to the water-cooled magnet coil, wherein the current intensity of the second current is greater than the current intensity of the first current;

[0025] The measured average temperature calculation unit is used to calculate the measured average temperature of the water-cooled magnet coil when the second current is passed based on the second current, the second voltage and the first resistance.

[0026] In the above-mentioned second aspect, the measured average temperature calculation unit is also used to: calculate the second resistance of the water-cooled magnet coil when the second current is passed according to the second current and the second voltage; and calculate the measured average temperature of the water-cooled magnet coil when the second current is passed based on the second resistance and the first resistance.

[0027] In the second aspect, the measured average temperature of the water-cooled magnet coil when the second current is applied is calculated based on the following formula: R2=R1[1+α(T-10)],

[0028] Wherein: R1 is the first resistor, R2 is the second resistor, U1 is the first voltage, I1 is the first current, U2 is the first voltage, I2 is the first current, α is the resistivity temperature coefficient of the water-cooled magnet coil, and T is the measured average temperature of the water-cooled magnet coil when the second current is passed.

[0029] In the above-mentioned second aspect, the fitting module is also used to: use the least squares method to fit the multiple different wall roughnesses and the multiple simulated average temperatures of the water-cooled magnet coils corresponding thereto to obtain a fitting function, wherein the fitting function satisfies the minimum sum of square errors of the extracted data.

[0030] In the above-mentioned second aspect, the heat transfer coefficient calculation module includes: a parameter calculation unit, which is used to substitute the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil into the wall conditions of the fluid-solid interface, and extract the heat flux and temperature parameters of the fluid-solid interface; a heat transfer coefficient calculation unit, which is used to calculate the average convective heat transfer coefficient of the interface between the water-cooled magnet coil and the fluid domain based on the heat flux and temperature parameters of the fluid-solid interface.

[0031] In the second aspect, the temperature parameters include the wall temperature and the average temperature of the water, and the heat transfer coefficient calculation unit is further configured to calculate the average convective heat transfer coefficient based on the following formula: q = h·(T W -T f ),

[0032] Where: q represents the heat flux, T W represents the wall temperature, T f represents the average temperature of water, and h represents the average convective heat transfer coefficient.

[0033] In the above second aspect, the system further includes: a temperature distribution analysis module, which is used to retrieve a temperature cloud map in the finite element analysis software to obtain the temperature distribution of the water-cooled magnet coil.

[0034] A third aspect of the present disclosure provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable by the processor. When the processor executes the computer program, the method described in the first aspect above is implemented.

[0035] A fourth aspect of the present disclosure provides a computer-readable storage medium having computer-executable instructions stored thereon. When the computer-executable instructions are executed by a processor, the processor is prompted to implement the method described in the first aspect above. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present disclosure or the technical solutions in the traditional technology, the following briefly introduces the drawings required for use in the embodiments or the description of the traditional technology. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0037] FIG1 is a schematic structural diagram of a water-cooled magnet coil assembled from a Bitter sheet and an insulating sheet in the related art;

[0038] FIG2 is a flow chart of a method for determining a convective heat transfer coefficient of a water-cooled magnet coil according to an embodiment of the present disclosure;

[0039] FIG3 is a schematic diagram of a three-dimensional model structure constructed in one embodiment of the present disclosure;

[0040] FIG4 is a schematic structural diagram of a system for determining a convective heat transfer coefficient of a water-cooled magnet coil according to an embodiment of the present disclosure;

[0041] FIG5 is a schematic structural diagram of a temperature measurement module according to an embodiment of the present disclosure;

[0042] FIG6 is a schematic structural diagram of a heat transfer coefficient calculation module according to an embodiment of the present disclosure;

[0043] 7 is a schematic structural diagram of a system for determining a convective heat transfer coefficient of a water-cooled magnet coil according to another embodiment of the present disclosure;

[0044] FIG8 is a schematic structural diagram of an electronic device according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0045] To make the objectives, technical solutions, and advantages of the present disclosure more clear, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the present disclosure. Obviously, the described embodiments are part of the embodiments of the present disclosure, but not all of the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present disclosure.

[0046] In this document, reference to the terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present disclosure. In this document, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0047] Although the terms "first" and "second" may be used herein to describe various features or elements, these features or elements should not be limited by these terms unless otherwise specifically indicated. These terms can be used to distinguish one feature or element from another feature or element. Thus, a first feature or element described below could be referred to as a second feature or element, and similarly, a second feature or element described below could be referred to as a first feature or element, without departing from the scope of this disclosure.

[0048] As shown in FIG2 , an embodiment of the present disclosure provides a method for determining a convective heat transfer coefficient of a water-cooled magnet coil, the method comprising steps S10 to S50 .

[0049] In step S10 , when a current of a predetermined current intensity is passed through the water-cooled magnet coil, the measured average temperature of the water-cooled magnet coil is obtained.

[0050] In step S20, a current of the predetermined current intensity is passed through a three-dimensional model of the water-cooled magnet coil in finite element analysis software, and a plurality of different wall roughnesses are set. Through simulation, a plurality of simulated average temperatures of the water-cooled magnet coil corresponding to the plurality of different wall roughnesses are obtained, wherein the measured average temperature of the coil is between the minimum value and the maximum value of the plurality of simulated average temperatures of the water-cooled magnet coil.

[0051] In this embodiment, the finite element analysis software used includes Fluent fluid simulation software.

[0052] In step S30 , a plurality of different wall surface roughness values ​​and their corresponding plurality of simulated average temperatures of the water-cooled magnet coils are fitted to obtain a fitting function.

[0053] Specifically, in this embodiment, ten different wall roughnesses can be set, and ten simulated average temperatures of the corresponding water-cooled magnet coils can be obtained through simulation. Then, these ten wall roughnesses and their corresponding ten simulated average temperatures of the water-cooled magnet coils are fitted to obtain a fitting function.

[0054] In step S40 , the measured average temperature of the water-cooled magnet coil is substituted into the fitting function to obtain the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil.

[0055] In step S50, the wall surface roughness corresponding to the measured average temperature of the water-cooled magnet coil is substituted into the finite element analysis software, and the convection heat transfer coefficient of the water-cooled magnet coil is obtained through simulation.

[0056] In this embodiment, by establishing a three-dimensional model of the coil and performing simulation calculations of the water-cooled magnet coil in finite element analysis software, multiple simulated average temperatures of the water-cooled magnet coil corresponding to multiple different wall roughnesses are obtained. Then, the multiple different wall roughnesses and their corresponding multiple simulated average temperatures of the water-cooled magnet coil are fitted to obtain a fitting function. This function is then combined with the measured average temperature of the coil obtained by experimental measurement to obtain the wall roughness corresponding to the measured average temperature of the coil. The obtained wall roughness can be used as the measured wall roughness under actual working conditions, ensuring that the simulated average temperature is the same as the measured average temperature, that is, the heat transfer coefficient is equal. Therefore, by substituting the measured wall roughness into the finite element analysis software for simulation, the convective heat transfer coefficient of the fluid-solid interface under actual working conditions can be obtained. The present disclosure obtains the convective heat transfer coefficient of the water-cooled magnet coil by combining numerical simulation with experiment. Compared with empirical formulas and experimental methods, this method improves the efficiency and accuracy of obtaining the convective heat transfer coefficient of the water-cooled magnet coil, while reducing research and development costs.

[0057] In one embodiment, step S10 includes steps S11 to S14.

[0058] In step S11, cooling water of a preset temperature is applied to the water-cooled magnet coil, and when the temperature of the water-cooled magnet coil is equal to the water temperature, a first voltage across the water-cooled magnet coil is measured when a first current is passed through the water-cooled magnet coil.

[0059] In this embodiment, the first current is a current with a low current intensity, and the current intensity thereof is in the range of about 100A to 200A.

[0060] In step S12, a first resistance of the water-cooled magnet coil at the preset temperature is calculated according to the first current and the first voltage.

[0061] In step S13 , a second voltage across the water-cooled magnet coil is measured when a second current is applied to the water-cooled magnet coil, wherein the current intensity of the second current is greater than the current intensity of the first current.

[0062] In step S14 , the measured average temperature of the water-cooled magnet coil when the second current is applied is calculated based on the second current, the second voltage, and the first resistance.

[0063] In this embodiment, the second current is a current with a high current intensity, and the current intensity thereof ranges from about 38900A to 40000A.

[0064] In one embodiment, step S14 includes: calculating a second resistance of the water-cooled magnet coil when the second current is passed according to the second current and the second voltage; and calculating a measured average temperature of the water-cooled magnet coil when the second current is passed based on the second resistance and the first resistance.

[0065] In one embodiment, the measured average temperature of the water-cooled magnet coil when the second current is applied is calculated based on the following formula: R2=R1[1+α(T-10)],

[0066] Wherein: R1 is the first resistor, R2 is the second resistor, U1 is the first voltage, I1 is the first current, U2 is the first voltage, I2 is the first current, α is the resistivity temperature coefficient of the water-cooled magnet coil, and T is the measured average temperature of the water-cooled magnet coil when the second current is passed.

[0067] Specifically, the actual process of measuring the average temperature of the coil is:

[0068] Apply cooling water at 10 degrees Celsius to the water-cooled magnet coil for half an hour, after which the temperature of the water-cooled magnet coil is equal to the temperature of the water, which is 10 degrees Celsius. Apply a small current of 100A to the water-cooled magnet coil, measure the voltage across the water-cooled magnet coil, and calculate the first resistance based on the measured voltage and current:

[0069] Then, a high current of 38900A is passed through the water-cooled magnet coil, and the corresponding second voltage is measured. Then, the second resistance of the water-cooled magnet coil at this time is calculated:

[0070] Then, the simultaneous equation: R2=R1[1+α(T-10)] is used to determine the measured average temperature of the water-cooled magnet coil when a current of 38900A is applied.

[0071] In one embodiment, the measured average temperature of the water-cooled magnet coil is between a minimum value and a maximum value of a simulated average temperature of the water-cooled magnet coil.

[0072] Specifically, if the measured average temperature of the water-cooled magnet coil is not between the minimum and maximum values ​​of the simulated average temperature of the water-cooled magnet coil, the wall roughness is changed so that the measured average temperature of the water-cooled magnet coil is between the minimum and maximum values ​​of the simulated average temperature of the water-cooled magnet coil.

[0073] In one embodiment, step S30 includes: using the least squares method to fit multiple different wall roughnesses and their corresponding multiple simulated average temperatures of the water-cooled magnet coils to obtain a fitting function, wherein the fitting function satisfies the minimum sum of square errors of the extracted data.

[0074] In this embodiment, the origin software can be used to fit the data using the least square method to obtain a fitting function.

[0075] In one embodiment, step S50 includes steps S51 and S52.

[0076] In step S51 , the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil is substituted into the wall condition of the fluid-solid interface to extract the heat flux and temperature parameters of the fluid-solid interface.

[0077] In step S52, based on the heat flux and temperature parameters of the fluid-solid interface, the average convective heat transfer coefficient of the interface between the water-cooled magnet coil and the fluid domain is calculated.

[0078] Specifically, the temperature parameters include the wall temperature and the average temperature of the water, and step S52 is implemented based on the following formula: q=h·(T W -T f ),

[0079] Where: q represents the heat flux, T W represents the wall temperature, T f represents the average temperature of water, and h represents the average convective heat transfer coefficient.

[0080] In one embodiment, the specific process of simulating the three-dimensional model of the water-cooled magnet coil in the finite element analysis software includes: establishing a three-dimensional model of the water-cooled magnet coil and the fluid domain, and performing boundary layer meshing on the fluid-solid interface of the three-dimensional model. For example, as shown in Figure 3, one 24th of the water-cooled magnet coil and the fluid domain is used as the three-dimensional model; performing hexahedral meshing on the fluid-solid interface of the three-dimensional model to obtain the meshed three-dimensional model.

[0081] Specifically, this embodiment establishes a 1 / 24 three-dimensional model of the water-cooled magnet coil and the fluid domain based on the number and size of the bit sheets and the insulating sheets, as shown in FIG3 . By simplifying the coil model based on the 12 fixed rod holes on the bitter sheet, the computational efficiency is improved.

[0082] Next, set the boundary conditions and structural property parameters for the 3D model. Boundary conditions include symmetry, voltage, inlet and outlet, and wall conditions. Structural property parameters, which account for the effects of temperature on properties, include viscosity, density, specific heat, thermal conductivity, and resistivity.

[0083] Then, the electric field, temperature, and fluid field simulation calculations are performed on the meshed 3D model to obtain the temperature distribution simulation results of the water-cooled magnet coil, including:

[0084] The k-epsolim turbulence model is used to perform electric field-temperature-fluid field simulation on the meshed 3D model to obtain the temperature distribution simulation results of the water-cooled magnet coil, where:

[0085] The governing equation for the electric field is: J=σE+J e ,

[0086] in: is the vector differential operator; J is the current density vector; Q j is the current source; σ is the conductivity; E is the electric field intensity vector; φ is the electric potential; J e is the external injection current density;

[0087] The governing equations for temperature and fluid fields are:

[0088] in: is the Hamiltonian operator; f is the unit fluid mass force; q is the volume heat flow of the magnet; ρ is the fluid density; v is the velocity vector of the fluid; p is the fluid pressure; μ is the fluid dynamic viscosity; e is the fluid internal energy; k is the fluid thermal conductivity; S is the part of the fluid mechanical energy converted into thermal energy under the combined action of the internal heat source of the fluid, t is time; T is temperature.

[0089] In this embodiment, the convective heat transfer coefficient is obtained by combining numerical simulation with experiments, and a joint simulation calculation of the electric field, temperature, and fluid field of the water-cooled magnet coil is carried out to obtain the simulated average temperature of the water-cooled magnet coil corresponding to different wall roughness.

[0090] In one embodiment, after step S50, the method further includes: retrieving a temperature cloud map in the finite element analysis software to obtain a temperature distribution of the water-cooled magnet coil.

[0091] In this embodiment, the distribution of the temperature, heat flux, etc. at each fluid-solid interface and the overall temperature distribution of the coil can be accurately obtained.

[0092] Each step of the above method can be performed by any suitable device that can perform the corresponding function. These devices may include various hardware and / or software components and / or modules, including but not limited to circuits, application specific integrated circuits (ASICs) or processors. It should be understood that although the various steps in the flowchart shown in the accompanying drawings are displayed in sequence as indicated by the arrows, these steps are not necessarily performed in sequence in the order indicated by the arrows. Unless clearly stated herein, the execution of these steps is not strictly limited in order and can be performed in other orders. Moreover, at least a portion of the steps in the flowchart shown in the accompanying drawings may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily performed at the same time, but can be performed at different times, and their execution order is not necessarily performed in sequence, but can be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.

[0093] 4 , an embodiment of the present disclosure further provides a system for determining the convective heat transfer coefficient of a water-cooled magnet coil, the system comprising a temperature measurement module 10 , a temperature simulation module 20 , a fitting module 30 , a wall roughness calculation module 40 and a heat transfer coefficient calculation module 50 .

[0094] The temperature measurement module 10 is used to obtain the measured average temperature of the water-cooled magnet coil when a current of a predetermined current intensity is passed through the water-cooled magnet coil. The temperature simulation module 20 is used to simulate the passage of a current of the predetermined current intensity through a three-dimensional model of the water-cooled magnet coil in finite element analysis software, and to set multiple different wall surface roughnesses. Through simulation, multiple simulated average temperatures of the water-cooled magnet coil corresponding to the multiple different wall surface roughnesses are obtained. The measured average temperature of the water-cooled magnet coil is between the minimum and maximum values ​​of the multiple simulated average temperatures of the water-cooled magnet coil. The fitting module 30 is used to fit the multiple different wall surface roughnesses and the multiple simulated average temperatures of the water-cooled magnet coil corresponding to each of them to obtain a fitting function. The wall surface roughness calculation module 40 is used to substitute the measured average temperature of the water-cooled magnet coil into the fitting function to obtain the wall surface roughness corresponding to the measured average temperature of the water-cooled magnet coil. The heat transfer coefficient calculation module 50 is used to substitute the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil into the finite element analysis software for simulation to obtain the convective heat transfer coefficient of the water-cooled magnet coil.

[0095] In one embodiment, as shown in FIG5 , the temperature measurement module 10 includes a temperature setting unit 101, a first resistance calculation unit 102, a current supply unit 103, and a measured average temperature calculation unit 104. The temperature setting unit 101 is configured to apply cooling water of a preset temperature to the water-cooled magnet coil and, when the temperature of the water-cooled magnet coil is equal to the water temperature, measure a first voltage across the water-cooled magnet coil when a first current is supplied to the water-cooled magnet coil. The first resistance calculation unit 102 is configured to calculate a first resistance of the water-cooled magnet coil at the preset temperature based on the first current and the first voltage. The current supply unit 103 is configured to measure a second voltage across the water-cooled magnet coil when a second current is supplied to the water-cooled magnet coil, wherein the second current has a greater current intensity than the first current. The measured average temperature calculation unit 104 is configured to calculate the measured average temperature of the water-cooled magnet coil when the second current is supplied based on the second current, the second voltage, and the first resistance.

[0096] In one embodiment, the measured average temperature calculation unit is further used to: calculate the second resistance of the water-cooled magnet coil when the second current is passed, based on the second current and the second voltage; and calculate the measured average temperature of the water-cooled magnet coil when the second current is passed, based on the second resistance and the first resistance.

[0097] In one embodiment, the measured average temperature of the water-cooled magnet coil when the second current is applied is calculated based on the following formula: R2=R1[1+α(T-10)],

[0098] Wherein: R1 is the first resistor, R2 is the second resistor, U1 is the first voltage, I1 is the first current, U2 is the first voltage, I2 is the first current, α is the resistivity temperature coefficient of the water-cooled magnet coil, and T is the measured average temperature of the water-cooled magnet coil when the second current is passed.

[0099] In one embodiment, the fitting module 30 is further configured to use a least squares method to fit different wall surface roughness values ​​and their corresponding simulated average temperatures of the water-cooled magnet coils to obtain a fitting function that minimizes the sum of squared errors of the extracted data.

[0100] In one embodiment, as shown in FIG6 , the heat transfer coefficient calculation module 50 includes a parameter calculation unit 501 and a heat transfer coefficient calculation unit 502. The parameter calculation unit 501 is configured to substitute the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil into the wall conditions of the fluid-solid interface to extract the heat flux and temperature parameters of the fluid-solid interface. The heat transfer coefficient calculation unit 502 is configured to calculate the average convective heat transfer coefficient of the interface between the water-cooled magnet coil and the fluid domain based on the heat flux and temperature parameters of the fluid-solid interface.

[0101] In one embodiment, the temperature parameters include the wall temperature and the average temperature of the water, and the convection heat transfer coefficient is calculated based on the following formula: q = h·(T W -T f ),

[0102] Where: q represents the heat flux, T W represents the wall temperature, T f represents the average temperature of water, and h represents the average convective heat transfer coefficient.

[0103] In one embodiment, as shown in Figure 7, the system further includes a temperature distribution analysis module 60. The temperature distribution analysis module 60 is used to retrieve a temperature cloud map in the finite element analysis software to obtain the temperature distribution of the water-cooled magnet coil.

[0104] The modules or units involved in the above-mentioned system for determining the convective heat transfer coefficient of a water-cooled magnet coil can be implemented by hardware or software. In particular, each block in the block diagram showing the system for determining the convective heat transfer coefficient of a water-cooled magnet coil, as well as the combination of blocks in the block diagram, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or can be implemented using a combination of dedicated hardware and computer instructions. It is understood that the name of a module or unit does not, in some cases, constitute a limitation on the module or unit itself. For example, a "temperature measurement module" can also be described as a "module for obtaining the measured temperature."

[0105] Figure 8 schematically illustrates the structure of an electronic device according to one embodiment of the present disclosure. The electronic device includes a memory, a processor, and a computer program stored in the memory and executable by the processor. When the processor executes the computer program, the method for determining the convective heat transfer coefficient of a water-cooled magnet coil described in the above embodiment is implemented. The electronic device 80 shown in Figure 8 is merely an example and should not limit the functionality or scope of use of the embodiments of the present disclosure.

[0106] As shown in FIG8 , electronic device 80 may be implemented as a computing device, such as a server device. Components of electronic device 80 may include, but are not limited to, at least one processor 81, at least one memory 82, and a bus 83 connecting various system components (including memory 82 and processor 81).

[0107] The bus 83 includes a data bus, an address bus, and a control bus.

[0108] The memory 82 may include a volatile memory, such as a random access memory (RAM) 821 and / or a cache memory 822 , and may further include a read-only memory (ROM) 823 .

[0109] The memory 82 may also include a program / utility 825 having a set (at least one) of program modules 824, such program modules 824 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0110] The processor 81 executes various functional applications and data processing by running computer programs stored in the memory 82, such as the medical image reconstruction method described in Example 1 of the present disclosure.

[0111] The electronic device 80 can also communicate with one or more external devices 84 (e.g., a keyboard, pointing device, etc.). This communication can occur via an input / output (I / O) interface 85. Furthermore, the model-generating device 80 can also communicate with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet) via a network adapter 86. As shown in FIG5 , the network adapter 86 communicates with other modules of the model-generating device 80 via a bus 83. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with the model-generating device 80, including but not limited to microcode, device drivers, redundant processors, external disk drive arrays, RAID (RAID) systems, tape drives, and data backup storage systems.

[0112] It should be noted that although several units / modules or sub-units / modules of the electronic device are mentioned in the detailed description above, this division is merely exemplary and not mandatory. In fact, according to the embodiments of the present disclosure, the features and functions of two or more units / modules described above can be embodied in one unit / module. Conversely, the features and functions of one unit / module described above can be further divided and embodied by multiple units / modules.

[0113] The present disclosure also provides a computer-readable storage medium having computer-executable instructions stored thereon. When executed by the processor, the computer-executable instructions cause the processor to implement the method for determining the convective heat transfer coefficient of a water-cooled magnet coil described in the above embodiment.

[0114] The aforementioned computer-readable storage medium may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or component, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more conductors, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present disclosure, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device, or component. In the present disclosure, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. This propagated data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable storage medium other than a computer-readable storage medium that can transmit, propagate, or convey a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the computer-readable storage medium may be conveyed using any suitable medium, including but not limited to wires, optical cables, RF (radio frequency), etc., or any suitable combination thereof.

[0115] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus the necessary general hardware platform, and of course can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present disclosure is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes a number of instructions for enabling a terminal device (which can be a mobile phone, computer, server, or network device, etc.) to execute the methods described in each embodiment of the present disclosure.

[0116] Although the embodiments of the present disclosure have been shown and described above, it is understood that the above embodiments are illustrative and are not to be construed as limitations on the present disclosure. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present disclosure.

Claims

1. A method for determining the convection heat transfer coefficient of a water-cooled magnet coil, characterized in that: The method comprises: When a current of a predetermined current intensity is passed through the water-cooled magnetic coil, obtaining a measured average temperature of the water-cooled magnetic coil; In finite element analysis software, a current of the predetermined current intensity is simulated to be passed through the three-dimensional model of the water-cooled magnet coil, and a plurality of different wall surface roughnesses are set, and a plurality of simulated average temperatures of the water-cooled magnet coil corresponding to the plurality of different wall surface roughnesses are obtained through simulation, wherein the measured average temperature of the water-cooled magnet coil is between a minimum value and a maximum value of the plurality of simulated average temperatures of the water-cooled magnet coil; Fitting the multiple different wall surface roughnesses and the multiple simulated average temperatures of the water-cooled magnet coils respectively corresponding thereto to obtain a fitting function; Substituting the measured average temperature of the water-cooled magnet coil into the fitting function to obtain the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil; The wall roughness corresponding to the measured average temperature of the water-cooled magnet coil is substituted into the finite element analysis software, and the convection heat transfer coefficient of the water-cooled magnet coil is obtained through simulation.

2. The method according to claim 1, characterized in that When a current of a predetermined current intensity is passed through the water-cooled magnetic coil, obtaining the measured average temperature of the water-cooled magnetic coil comprises: Applying cooling water of a preset temperature to the water-cooled magnet coil, and measuring a first voltage across the water-cooled magnet coil when a first current is passed through the water-cooled magnet coil when the temperature of the water-cooled magnet coil is equal to the temperature of the cooling water; calculating a first resistance of the water-cooled magnet coil at the preset temperature according to the first current and the first voltage; measuring a second voltage across the water-cooled magnet coil when a second current is passed through the water-cooled magnet coil, wherein the current intensity of the second current is greater than the current intensity of the first current; The measured average temperature of the water-cooled magnet coil when the second current is passed is calculated based on the second current, the second voltage, and the first resistance.

3. The method according to claim 2, characterized in that The step of calculating the measured average temperature of the water-cooled magnet coil when the second current is applied based on the second current, the second voltage and the first resistance includes: calculating, according to the second current and the second voltage, a second resistance of the water-cooled magnet coil when the second current is passed; Based on the second resistance and the first resistance, the measured average temperature of the water-cooled magnet coil when the second current is passed is calculated.

4. The method according to claim 3, characterized in that The measured average temperature of the water-cooled magnet coil when the second current is applied is calculated based on the following formula: R2=R1[1+α(T-10)], Wherein: R1 is the first resistor, R2 is the second resistor, U1 is the first voltage, I1 is the first current, U2 is the first voltage, I2 is the first current, α is the resistivity temperature coefficient of the water-cooled magnet coil, and T is the measured average temperature of the water-cooled magnet coil when the second current is passed.

5. The method according to claim 1, characterized in that The fitting of the plurality of different wall surface roughnesses and the plurality of simulated average temperatures of the water-cooled magnet coils respectively corresponding thereto to obtain a fitting function comprises: The plurality of different wall surface roughnesses and the plurality of simulated average temperatures of the water-cooled magnet coils respectively corresponding thereto are fitted using the least square method to obtain a fitting function, wherein the fitting function satisfies the minimum sum of square errors of the extracted data.

6. The method according to claim 1, characterized in that Substituting the wall surface roughness corresponding to the measured average temperature of the water-cooled magnet coil into the finite element analysis software and obtaining the convection heat transfer coefficient of the water-cooled magnet coil by simulation includes: Substituting the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil into the wall condition of the fluid-solid interface to extract the heat flux and temperature parameters of the fluid-solid interface; Based on the heat flux and temperature parameters of the fluid-solid interface, the average convection heat transfer coefficient of the interface between the water-cooled magnet coil and the fluid domain is calculated.

7. The method according to claim 6, characterized in that The temperature parameters include the wall temperature and the average temperature of the water. The calculation of the average convective heat transfer coefficient of the interface between the water-cooled magnet coil and the fluid domain based on the heat flux and temperature parameters of the fluid-solid interface includes calculating the average convective heat transfer coefficient based on the following formula: q=h·(T W -T f ), Where: q represents the heat flux, T W is the wall temperature, T f represents the average temperature of water, and h represents the average convection heat transfer coefficient.

8. The method according to claim 1, characterized in that After substituting the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil into the finite element analysis software and obtaining the convective heat transfer coefficient of the water-cooled magnet coil through simulation, the method also includes: calling up a temperature cloud map in the finite element analysis software to obtain the temperature distribution of the water-cooled magnet coil.

9. A system for determining the convection heat transfer coefficient of a water-cooled magnet coil, characterized in that: The system comprises: A temperature measurement module, used for obtaining the measured average temperature of the water-cooled magnetic coil when a current of a predetermined current intensity is passed through the water-cooled magnetic coil; A temperature simulation module, used for simulating the current of the predetermined current intensity to be passed through the three-dimensional model of the water-cooled magnet coil in the finite element analysis software, and setting a plurality of different wall surface roughnesses, and obtaining a plurality of simulated average temperatures of the water-cooled magnet coil corresponding to the plurality of different wall surface roughnesses through simulation, wherein the measured average temperature of the water-cooled magnet coil is between a minimum value and a maximum value of the plurality of simulated average temperatures of the water-cooled magnet coil; A fitting module, used for fitting the multiple different wall surface roughnesses and the multiple simulated average temperatures of the water-cooled magnet coils respectively corresponding thereto to obtain a fitting function; A wall surface roughness calculation module, used for substituting the measured average temperature of the water-cooled magnet coil into the fitting function to obtain the wall surface roughness corresponding to the measured average temperature of the water-cooled magnet coil; The heat transfer coefficient calculation module is used to substitute the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil into the finite element analysis software, and obtain the convection heat transfer coefficient of the water-cooled magnet coil through simulation.

10. The system according to claim 9, characterized in that The temperature measurement module comprises: a temperature setting unit, configured to apply cooling water of a preset temperature to the water-cooled magnet coil, and, when the temperature of the water-cooled magnet coil is equal to the temperature of the cooling water, measure a first voltage across the water-cooled magnet coil when a first current is passed through the water-cooled magnet coil; a first resistance calculation unit, configured to calculate a first resistance of the water-cooled magnet coil at the preset temperature according to the first current and the first voltage; The current supply unit is used to measure a second voltage across the water-cooled magnet coil when a second current is supplied to the water-cooled magnet coil, wherein the current intensity of the second current is greater than the current intensity of the first current; The measured average temperature calculation unit is used to calculate the measured average temperature of the water-cooled magnet coil when the second current is passed based on the second current, the second voltage and the first resistance.

11. The system according to claim 10, characterized in that The measured average temperature calculation unit is also used for: calculating, according to the second current and the second voltage, a second resistance of the water-cooled magnet coil when the second current is passed; Based on the second resistance and the first resistance, the measured average temperature of the water-cooled magnet coil when the second current is passed is calculated.

12. The method according to claim 11, characterized in that The measured average temperature of the water-cooled magnet coil when the second current is applied is calculated based on the following formula: R2=R1[1+α(T-10)], Wherein: R1 is the first resistor, R2 is the second resistor, U1 is the first voltage, I1 is the first current, U2 is the first voltage, I2 is the first current, α is the resistivity temperature coefficient of the water-cooled magnet coil, and T is the measured average temperature of the water-cooled magnet coil when the second current is passed.

13. The method according to claim 9, characterized in that The fitting module is also used for: The plurality of different wall surface roughnesses and the plurality of simulated average temperatures of the water-cooled magnet coils respectively corresponding thereto are fitted using the least square method to obtain a fitting function, wherein the fitting function satisfies the minimum sum of square errors of the extracted data.

14. The system of claim 9, wherein: The heat transfer coefficient calculation module includes: A parameter calculation unit, used to substitute the wall roughness corresponding to the measured average temperature of the water-cooled magnet coil into the wall condition of the fluid-solid interface, and extract the heat flux and temperature parameters of the fluid-solid interface; The heat transfer coefficient calculation unit is used to calculate the average convection heat transfer coefficient of the interface between the water-cooled magnet coil and the fluid domain based on the heat flux and temperature parameters of the fluid-solid interface.

15. The system of claim 14, wherein: The temperature parameters include the wall temperature and the average temperature of the water. The heat transfer coefficient calculation unit is further used to calculate the average convection heat transfer coefficient based on the following formula: q = h·(T W -T f ), Where: q represents the heat flux, T W is the wall temperature, T f represents the average temperature of water, and h represents the average convection heat transfer coefficient.

16. The system of claim 9, wherein: The system further comprises: The temperature distribution analysis module is used to retrieve the temperature cloud map in the finite element analysis software to obtain the temperature distribution of the water-cooled magnet coil.

17. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable by the processor, wherein when the processor executes the computer program, the method according to any one of claims 1 to 8 is implemented.

18. A computer-readable storage medium having computer-executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the method according to any one of claims 1 to 8.

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