CN116341324B - Three-dimensional temperature field of conduction cooling superconducting cavity and electromagnetic loss reconstruction method - Google Patents
Three-dimensional temperature field of conduction cooling superconducting cavity and electromagnetic loss reconstruction method Download PDFInfo
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Abstract
The invention discloses a three-dimensional temperature field of a conduction cooling superconducting cavity and an electromagnetic loss reconstruction method, which comprises the following steps: 1) Establishing a forward model and a reverse model of the conduction cooling superconducting cavity; the calculation domain of the forward model comprises a superconducting cavity region omega for calculating a temperature field 1 Vacuum area Ω for calculating electromagnetic field 2 ，Ω 1 And omega 2 Is Γ 2 ；Γ 1 Is the superconducting cavity outer surface Γ 3 Is a side surface area of the superconducting cavity beam tube; according to Γ 1 、Γ 3 Temperature determination Γ at 3 Is used for determining the wall temperature boundary condition; will be gamma 1 The place is set as an adiabatic boundary condition; will be gamma 2 The heat flux density at the position is set as q; 2) Solving the forward model to obtain gamma 2 Omega corresponding to heat flow density of different distribution 1 Temperature T of (2); a solving method of the reverse model is optimized according to T and q; 3) Reconstruction Γ using inverse model 2 A heat flux density function thereon; 4) Modifying Γ in a forward model based on a heat flux density function 2 Boundary conditions at which a three-dimensional temperature field is reconstructed.
Description
Technical Field
The invention relates to a three-dimensional temperature field and electromagnetic loss reconstruction technology of a conduction cooling superconducting cavity based on temperature field inversion, which is used for research and development test of the conduction cooling superconducting cavity, temperature monitoring and fault diagnosis during stable operation.
Background
Due to its excellent properties, the application of superconducting accelerators is gradually widened to industrial wastewater treatment, cellulose manufacture, and medical (isotope) production. Compared with the traditional liquid helium soaking cooling, the superconducting cavity is cooled by using a conduction cooling mode of a small refrigerator, and the superconducting cavity has the advantages of compact structure, high economy, reliability, easiness in maintenance and the like. These advantages make it of great advantage in industry and the like. As the cooling capacity of small refrigerators is generally small, about 2W@4.2K, there is a higher demand for the heat transfer capacity of the cooling structure. The reliable and efficient conduction cooling structure is a key factor for ensuring the temperature stability and normal operation of the superconducting cavity.
Unlike liquid helium soaking cooling, conduction cooling can lead to the unavoidable existence of a large temperature gradient of a superconducting cavity, and meanwhile, due to limited heat transfer capacity, the heat transfer speed of the superconducting cavity after local quench is obviously lower than boiling heat exchange during soaking, the heat transfer path is longer, the temperature of more areas can be increased, and the quench risk is increased.
In addition, accurate measurement of superconducting cavity electromagnetic loss is a key parameter for evaluating superconducting cavity performance (Q value). When liquid helium is used for soaking and cooling, the electromagnetic loss is measured by the flow of helium gas evaporated from a helium pool, and the measurement result of the method is generally high in reliability. The measurement of electromagnetic losses in superconducting cavities is also a critical loop when using conduction cooling, and the accuracy and reliability of new measurement schemes need to be evaluated. The work is not developed in China at present and is in a starting exploration stage.
At present, the low-temperature system of the superconducting accelerator is mainly a large helium low-temperature system, the superconducting cavity is soaked and cooled by liquid helium, the stable operation of the superconducting cavity is ensured by large cold quantity and efficient boiling heat transfer, and the heat transfer process of the superconducting cavity is not much concerned when in actual work, so that the technology has less application in the superconducting accelerator. The technology has many application scenarios in conduction cooling superconducting cavities.
Disclosure of Invention
In order to accurately judge the temperature distribution of the whole conduction cooling superconducting cavity in the cooling and quench process, the invention provides a three-dimensional temperature field of the conduction cooling superconducting cavity and an electromagnetic loss reconstruction method. The present invention has developed a technique for reverse reconstruction of the temperature field and boundary conditions (electromagnetic losses at the inner surface of the superconducting cavity) of the superconducting cavity in time and space coordinates by means of limited temperature sensor data. The temperature field and electromagnetic loss reconstruction technology of the conduction cooling superconducting cavity based on temperature field inversion can obtain richer physical parameters, such as electromagnetic loss and temperature distribution in the superconducting cavity, diffusion speed of a quench zone after quench and the like, according to limited measurement. The technology is applied to various fields including aerospace, metallurgy, engine manufacturing and other engineering fields, and equipment improvement and related process improvement are promoted.
The invention can be used for research and development test of the conduction cooling superconducting cavity, monitoring in the running process and fault diagnosis, and provides powerful software support for the development of the conduction cooling superconducting cavity technology.
The technical scheme of the invention is as follows:
a three-dimensional temperature field of a conduction cooling superconducting cavity and an electromagnetic loss reconstruction method comprise the following steps:
1) Establishing a forward model and a reverse model of the conduction cooling superconducting cavity; the calculation domain of the forward model comprises a superconducting cavity region omega for calculating a temperature field 1 Vacuum area Ω for calculating electromagnetic field 2 ，Ω 1 And omega 2 Is Γ 2 ；Γ 1 Is the outer surface of the superconducting cavity, on which a plurality of temperature sensors are arranged, Γ 3 Is a side surface area of the superconducting cavity beam tube; according to Γ 1 Measured values Γ of the sensor arranged thereon 3 Temperature measurements at interface locations determine Γ 3 A first type of boundary condition; will be gamma 1 The position is set as an adiabatic boundary condition, namely a second type boundary condition; will be gamma 2 The heat flux density at the position is set as q;
2) Solving the forward model by using a finite difference method to obtain gamma 2 Omega corresponding to heat flow density of different distribution 1 Temperature data T of (2); determining Γ for inverse model solution from the temperature data T and heat flux density data q 1 The position and iteration parameters of the sensors to be arranged are optimized, and the solving method of the reverse model is optimized;
3) T determined based on step 2) 1 Temperature measured by a temperature sensor on the boundary, reconstructing Γ using the inverse model 2 The heat flux density function q (x, y, z, t) is the electromagnetic loss distribution of the superconducting cavity;
4) Based on gamma 2 The heat flux density function q (x, y, z, t) on the forward model modifies Γ 2 And reconstructing a three-dimensional temperature field of the conduction cooling superconducting cavity by using the forward model.
Further, reconstructing Γ using the inverse model 2 Heat flux density function q (x, y, z, t) on Ω 1 The method of the internal temperature field is as follows:
21 Acquiring superconducting cavity outer surface T) 1 Temperature data measured by a temperature sensor arranged aboveT n Is->Temperature data after noise removal; then find the q (x, y, z, t) function in the solution space ψ such that the equation +.>Hold in pi; f is an abstract function of the heat conduction equation in the reverse model; />Ψ＝L 2 (0,t；H 1 (T 2 ) A) is provided; wherein N represents the number of temperature measuring points;
22 According to the q (x, y, z, t) function obtained in step 21) as Γ 2 Boundary conditions at; at Ω 1 Is solved by using a heat conduction equation (the boundary condition of the forward model is modified) to obtain omega 1 Temperature of the domain, finish Ω 1 And reconstructing the temperature field in the inner part.
Further, regularization is used to minimize the objective function Solving to obtain a heat flow density function q (x, y, z, t); wherein beta is more than or equal to 0.
Further, an iterative regularization calculation method adopting a conjugate gradient method is adopted to select an objective function when beta=0The heat flux density function q (x, y, z, t) is obtained by the minimization solution; the convergence criterion of the conjugate gradient method is that the residual error between the predicted temperature and the actual measured temperature of the inverse model is minimum.
Further, the method comprises the steps of,delta is the upper noise bound.
Further, the reverse model is utilized to simulate the quench process of the conduction cooling superconducting cavity, and the method comprises the following steps:
61 Using the inverse model and Γ 1 Calculating the temperature and heat flux density value at each time t from the temperature data measured by the temperature sensor arranged above;
62 Calculating Γ) 2 A quench zone on the upper part, and locating the position of the beginning of the quench; marking position coordinates with the temperature higher than 9.2K according to the temperature calculated in the step 61), namely a quench zone;
63 Calculating the quench propagation speed according to the boundary position coordinates of the two-time quench areas;
64 According to the reconstructed temperature data, calculating to obtain the maximum temperature distribution and the temperature gradient of the superconducting cavity corresponding to the conducting structure and the total quench time of the superconducting cavity, and evaluating the heat conduction capacity of the conducting structure by taking the maximum temperature distribution and the temperature gradient as the standard.
Further, the cooling process of the conduction cooling superconducting cavity is simulated by using the reverse model, and the method comprises the following steps:
71 Using the inverse model and T 1 The temperature data measured by the temperature sensor arranged above calculate the temperature at each moment t, and the change relation of the temperature field of the whole superconducting cavity along with time is reversely constructed;
72 Calculating stress distribution of the superconducting cavity at each moment t according to the change relation of the temperature field of the superconducting cavity with time obtained in the step 71), and marking the position with the maximum stress;
73 Judging whether the stress distribution exceeds a set value, if so, giving an early warning; and depending on the specific value and location of the stress,
the heater power at the corresponding position is controlled, and the stress at the position is reduced.
The invention has the following advantages:
the temperature field and electromagnetic loss reconstruction technology of the conduction cooling superconducting cavity based on temperature field inversion can obtain richer physical parameters according to limited measurement, and provides a powerful tool for research, development and test and stable operation of the conduction cooling superconducting cavity. The temperature can be monitored in real time in the testing and running processes of the conduction cooling superconducting cavity, richer physical images are provided, and fault diagnosis can be performed. The application of the technology can optimize the layout of the sensor, provide reliable data support for the arrangement of the sensor and the temperature control of the superconducting cavity, and further reduce the experiment cost.
Drawings
FIG. 1 is a block diagram of a conduction cooled superconducting cavity.
FIG. 2 is a flow chart of the method of the present invention.
FIG. 3 is a schematic diagram of a quarter-domain calculation.
Detailed Description
The invention will now be described in further detail with reference to the accompanying drawings, which are given by way of illustration only and are not intended to limit the scope of the invention.
The conduction cooling superconducting cavity structure is shown in fig. 1, and the invention takes the superconducting cavity and the conduction cooling structure thereof as research objects to establish an inverse problem mathematical model based on a heat conduction equation, namely an inverse model. The specific technical scheme is as follows:
and (3) establishing a forward model and a reverse model, wherein the forward model is shown in fig. 2.
The computational domain of the model is shown in fig. 3:
characteristic 1:
in FIG. 3, Ω 1 Is superconducting cavity region, temperature field, Ω 2 Is the vacuum area inside the superconducting cavity, is electromagnetic field, Ω 1 And omega 2 Is Γ 2 ，Γ 2 The second type of boundary condition, i.e., adiabatic boundary condition, is the heat flux density q (x, y, z, t). T (T) 1 For the outer surface of the superconducting cavity, a certain number of temperature sensors are arranged, T 3 Since the electromagnetic loss of the area is generally small, the area is defined as a fixed wall temperature boundary condition, and the measured value of the arranged sensor is taken. Γ -shaped structure 2 There is electromagnetic loss, q (x, y, z, t).
Based on T 1 Temperature of boundary measurement is inverted to obtain T 2 Accurate heat flux density q (x, y, z, t) not directly measurable at boundary and whole temperature field Ω 1 The temperature distribution of (2) is an inverse problem of three-dimensional heat conduction. This problem assumes that the relevant physical parameters (i.e. the parameters of thermal conductivity, density, heat capacity, etc. of the material present in the thermal conduction equation) are known and accurate, and may lead to a non-unique resulting solution, i.e. q (x, y, z, t), based on limited measurement data. Meanwhile, a minute measurement error of the sensor may cause a large deviation of the estimated value, so that the problem is an ill-posed problem.
At Ω 1 In the above, the heat conduction process can be described as:
where T represents a continuous function of temperature in relation to time and space coordinates, ρ, C, λ are density, heat capacity and thermal conductivity, respectively, and T is the final time. At low temperatures, the physical properties of the material vary greatly with temperature, so the physical properties are a function of temperature. q (x, y, z, t) represents a group defined as Γ 2 The heat flux density function, the value of which is a function of time and space coordinates, is the second kind of boundary condition of the equation; the problem is that it is appropriate that the solution is present and unique after the initial conditions and boundary conditions are determined.
Characteristic 2:
after the forward model is established, a finite difference method is used for solving a heat conduction equation of the forward model, and the heat flow density q and the temperature T under the determined boundary condition can be obtained. The data are used for numerical experiments to provide guidance for verification of the reverse model and selection of specific parameters. In addition, the location of the temperature point selection needs to be determined through numerical experiments to guide the sensor arrangement in experimental testing. The accurate forward model and the accurate solving method are the basis for providing accurate data, and the convergence standard of the numerical solution is required to be 10 -6 。
Γ in forward model 1 The temperature data at which is unknown, the forward model is modeled under a given determined boundary condition (Γ 1 ,Γ 2 ,Γ 3 ) After that, omega can be calculated 1 Temperature. Wherein Γ is 1 、Γ 3 Boundary conditions at the point remain unchanged, modify Γ 2 Q at. Omega thus obtained 1 Temperature and given q (Γ 2 Where) are in one-to-one correspondence.
Characteristic 3: reverse model creation and solution
The thermal conductivity anti-problems here are known physical properties, initial field temperature distribution and Γ 3 Temperature change with time at a temperature based on Γ 1 Reconstructing Γ from measured temperature data 2 The heat flux density functions q (x, y, z, t) and Ω 1 And (3) an internal overall temperature field. Measuring onlyObtain gamma 1 Temperature data of finite place, which can be based on Γ using inverse model 1 The temperature data with limited positions are calculated to obtain q and omega 1 Temperature data on the domain. The physical parameters are properties of the material, and are determined by measurement or physical library. The initial field refers to Ω 1 The total temperature distribution of the domain at the initial moment, which is generally a stable field distribution, changes in temperature after the electromagnetic field is applied, and the initial field at this time is the temperature field immediately before the electromagnetic field is applied.
Assume thatT n Noiseless measured temperature data representing the actual physical process, < >>Actual observation data representing the upper bound of noise as delta, i.e. superconducting cavity outer surface Γ 1 Temperature data measured by a temperature sensor arranged above; />The temperature data after noise removal is T n . The inverse problem is to solve the following equation:
the solution is to find the appropriate q (x, y, z, t) function in the solution space ψ so that the abstract equation holds in ζ. F is an abstract function representing a heat conduction equation. q (x, y, z, t) is the superconducting cavity Γ 2 And the heat flow density value of the position (x, y, z) at the time t in the upper space-time coordinate. T (T) n And (3) withThe relation of (2) is:
in the actual measurement process, T n While q (x, y, z, t) is a function of both temperature and space. ψ, pi should be spatially square integrable:
Ψ＝L 2 (0,t；H 1 (Γ 2 ))
wherein N represents the number of temperature measuring points, and i represents the number of measuring points; l (L) 2 Is a mathematical representation of the square integrable space.
For the inverse problem described above, the heat flux density function q (x, y, z, t) can be obtained by solving by minimizing the objective function using a regularization method. In this problem, the objective function is:
phi (q) contains the fitting error of the data and the concussion of the estimated quantity caused by discomfort. The estimation quality of the regularized solution based on Tikhonov has a great relation with the choice of beta. Here, an iterative regularization calculation method of conjugate gradient method is adopted, and an objective function when β=0 is selected. The objective function of interest at this time is reduced to:
when the conjugate gradient method is used, the regularization parameter in the optimization problem is the iteration number, and the discomfort of the inverse problem is processed by adopting iteration stopping. The convergence criterion of the method is that the residual error between the predicted temperature of the model and the actual measured temperature is minimum, and when the temperature residual error is approximately equal to the error, the iterative process is stopped. Contrast Γ 2 The influence rule of different heat flux densities on the iteration times is provided. Since the practical heat flux density is consistent with the approximate distribution of the space, q is selected in the forward modelFunctions that are similar are distributed.
Solving to obtainAfter the corresponding q (x, y, z, t), q (x, y, z, t) is taken as Γ 2 Boundary conditions at Ω 1 Can be solved by using a heat conduction equation (forward model) to obtain omega 1 And (3) the temperature of the domain, and completing the three-dimensional temperature field reconstruction of the superconducting cavity.
Characteristic 4:
application of reverse model in cooling process
In the cooling process of the superconducting cavity, the gamma is 2 Since the heat flux density is 0, the problem is simplified and the solution is relatively easy. The temperature field change relation of the whole superconducting cavity along with time is reversely constructed through high-resolution temperature data, so that:
(1) Calculating stress distribution of the superconducting cavity at each moment, and marking the position with the maximum stress;
(2) Judging whether the stress distribution exceeds a set value, if so, giving an early warning;
(3) And controlling the power of the heater at the corresponding position according to the specific value and the position of the stress, and reducing the stress at the position.
And 5. The characteristics are as follows:
application of reverse model in quench process
Quench of the superconducting cavity generally occurs in testing and failure. During the test, the inverse model and the surface Γ are utilized 1 The temperature data measured by the temperature sensor arranged above may be:
(1) Calculating the temperature and heat flux density distribution q (x, y, z, t) at each moment;
(2) Calculating Γ 2 A quench zone on the upper part, and locating the position of the beginning of the quench; and marking position coordinates with the temperature higher than 9.2K according to the calculated temperature, namely a quench area. Since the temperature data is updated after each time interval, the location of the quench zone is also updated in real time.
(3) Calculating the speed of quench propagation; quench rate is based on boundary position of the two-time quench zoneAnd (5) performing label calculation. Quench zone is Ω 3 (t)，Ω 3 The boundary of (t) is denoted as S (x, y, z, t). Then>Quench rate of +.>
(4) And evaluating the heat conduction capacity of the conduction structure, and calculating the maximum temperature distribution, the temperature gradient and the total quench time of the superconducting cavity corresponding to the conduction structure according to the reconstructed temperature data, wherein the maximum temperature distribution, the temperature gradient and the total quench time of the superconducting cavity are used as the standard to evaluate the heat conduction capacity of the conduction structure.
Application of reverse model in normal operation:
(1) Monitoring the change in q (x, y, z, t) as a function of temperature;
(2) After the local temperature rise occurs, diagnosing the cause of the temperature rise, whether the electromagnetic loss causes the cooling capacity to be reduced or not;
(3) Early warning the fluctuation q (x, y, z, t) of electromagnetic loss, and setting an early warning value q 0 Reconstructed q (x, y, z, t) and q 0 The difference delta q is a monitoring quantity, and when delta q is higher than a set value, an early warning is sent out;
(4) And drawing a real-time three-dimensional temperature and electromagnetic loss distribution image.
The reverse model can be implanted into a low-temperature control system of the conduction cooling superconducting cavity after testing and perfecting relevant parameters, gives real-time temperature and electromagnetic loss inversion results, and provides powerful software support for testing and running of the conduction cooling superconducting cavity.
Although specific embodiments of the invention have been disclosed for illustrative purposes, it will be appreciated by those skilled in the art that the invention may be implemented with the help of a variety of examples: various alternatives, variations and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will have the scope indicated by the scope of the appended claims.
Claims (6)
1. A three-dimensional temperature field of a conduction cooling superconducting cavity and an electromagnetic loss reconstruction method comprise the following steps:
1) Establishing a forward model and a reverse model of the conduction cooling superconducting cavity; the calculation domain of the forward model comprises a superconducting cavity region omega for calculating a temperature field 1 Vacuum area Ω for calculating electromagnetic field 2 ，Ω 1 And omega 2 Is Γ 2 ；Γ 1 Is the outer surface of the superconducting cavity, on which a plurality of temperature sensors are arranged, Γ 3 Is a side surface area of the superconducting cavity beam tube; according to Γ 1 Measured values Γ of the sensor arranged thereon 3 Temperature measurements at interface locations determine Γ 3 A first type of boundary condition; will be gamma 1 The position is set as an adiabatic boundary condition, namely a second type boundary condition; will be gamma 2 The heat flux density at the position is set as q;
2) Solving the forward model by using a finite difference method to obtain omega corresponding to heat flow densities of different distributions at Γ2 1 Temperature data T of (2); determining Γ for inverse model solution from the temperature data T and heat flux density data q 1 The position and iteration parameters of the sensors to be arranged are optimized, and the solving method of the reverse model is optimized;
3) Γ determined based on step 2) 1 Temperature measured by a temperature sensor on the boundary, reconstructing Γ using the inverse model 2 Heat flux density function q (x, y, z, t) on Ω 1 The temperature field in the superconducting cavity, and the current density function q (x, y, z, t) is the electromagnetic loss distribution of the superconducting cavity; wherein, reconstruct Γ 2 Heat flux density function q (x, y, z, t) on Ω 1 The method of the internal temperature field is as follows: 31 Acquiring superconducting cavity outer surface Γ 1 Temperature data measured by a temperature sensor arranged aboveT n Is->Temperature data after noise removal; then find the q (x, y, z, t) function in the solution space ψ such that the equation +.>Hold in pi; f is an abstract function of the heat conduction equation in the reverse model; />Ψ＝L 2 (0，t；H 1 (Γ 2 ) A) is provided; wherein N represents the number of temperature measuring points; 32 (r) as Γ) according to the q (x, y, z, t) function obtained in step 31) 2 Boundary conditions at; at Ω 1 Is solved by using a heat conduction equation to obtain omega 1 Temperature of the domain, finish Ω 1 Reconstructing the internal temperature field;
4) Based on gamma 2 The heat flux density function q (x, y, z, t) on the forward model modifies Γ 2 And reconstructing a three-dimensional temperature field of the conduction cooling superconducting cavity by using the forward model.
2. The method of claim 1, wherein the regularization method is used by minimizing an objective functionSolving to obtain a heat flow density function q (x, y, z, t); wherein beta is more than or equal to 0.
3. The method of claim 2, wherein the iterative regularization calculation method using conjugate gradient method selects an objective function with β=0The heat flux density function q (x, y, z, t) is obtained by the minimization solution; by conjugate gradient methodsThe convergence criterion is that the residual error between the predicted temperature and the actual measured temperature of the inverse model is minimal.
4. The method of claim 1, wherein the step of determining the position of the substrate comprises,delta is the upper noise bound.
5. The method according to any one of claims 1 to 4, characterized in that the quench process of the conduction-cooled superconducting cavity is simulated by means of the inverse model by:
61 Using the inverse model and Γ 1 Calculating the temperature and heat flux density value at each time t from the temperature data measured by the temperature sensor arranged above;
62 Calculating Γ) 2 A quench zone on the upper part, and locating the position of the beginning of the quench; marking position coordinates with the temperature higher than 9.2K according to the temperature calculated in the step 61), namely a quench zone;
63 Calculating the quench propagation speed according to the boundary position coordinates of the two-time quench areas;
64 According to the reconstructed temperature data, calculating to obtain the maximum temperature distribution and the temperature gradient of the superconducting cavity corresponding to the conducting structure and the total quench time of the superconducting cavity, and evaluating the heat conduction capacity of the conducting structure by taking the maximum temperature distribution and the temperature gradient as the standard.
6. The method according to any one of claims 1 to 4, wherein the cooling process of the conduction cooling superconducting cavity is simulated by using the inverse model, and the method comprises the following steps:
71 Using the inverse model and Γ 1 The temperature data measured by the temperature sensor arranged above calculate the temperature at each moment t, and the change relation of the temperature field of the whole superconducting cavity along with time is reversely constructed;
72 Calculating stress distribution of the superconducting cavity at each moment t according to the change relation of the temperature field of the superconducting cavity with time obtained in the step 71), and marking the position with the maximum stress;
73 Judging whether the stress distribution exceeds a set value, if so, giving an early warning; and controlling the heater power at the corresponding position according to the specific value and the position of the stress, and reducing the stress at the position.
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