Method for correcting precision of numerical model of 2K ultralow-temperature heat exchanger by using normal-temperature data

Abstract

The invention discloses a method for correcting the precision of a numerical model of a 2K ultralow-temperature heat exchanger by using normal-temperature data. The method comprises the following steps of: 1) determining an input parameter vector P1 under a normal-temperature working condition and an input parameter vector P2 under a low-temperature working condition, which have the greatest influence on an output result, by using a Sobol method; 2) obtaining the uncertainty delta in1 corresponding to the P1 and the uncertainty delta in2 corresponding to the P2 according to priori knowledge; 3) obtaining the experimental uncertainty delta D1 of the normal temperature test; 4) calculating numerical method uncertainty delta num1 and delta num2 under the normal temperature condition and the low temperature condition; 5) calculating the uncertainty delta model of the model structure; (6) obtaining the complete uncertainty of the numerical simulation value under the low-temperature working condition by utilizing the model structure uncertainty delta model and combining delta num2 and delta in2; and 7) correcting an output result of the 2K ultralow-temperature heat exchanger numerical model according to the intact uncertainty.

Description

Technical Field

[0001] The present invention belongs to the field of simulation technology, and relates to a technology for correcting the accuracy of a numerical model of a 2K superfluid helium cryogenic heat exchanger based on cheap and easily available normal temperature test data, and in particular to a method for correcting the accuracy of a numerical model of a 2K ultra-low temperature heat exchanger using normal temperature test data, which is used for the design and optimization of a 2K superfluid helium cryogenic heat exchanger, which is a key core component of a large superconducting cryogenic system. Background Art

[0002] The 2K helium cryogenic system is responsible for providing ultra-low temperature environment for large scientific equipment such as large superconducting accelerators / large superconducting fusion reactors. The 2K superfluid helium cryogenic heat exchanger (hereinafter referred to as 2K heat exchanger) is Figure 1 As shown in the figure, it is one of the core components in the 2K helium cryogenic system. It is usually located before the last stage throttle valve of the 2K helium cryogenic system. It is responsible for recovering the coldness of the 2K helium vapor and improving the liquid output rate of the last stage throttle valve. The heat exchange efficiency and low-pressure side pressure drop of the 2K heat exchanger are two core performance indicators, which directly affect the liquid output rate and the load of the rotating machinery on the low-pressure side.

[0003] At present, there have been some research works on 2K heat exchangers, and research has been carried out on 2K heat exchangers from the aspects of design, optimization, manufacturing, testing, etc. However, there are still several problems that are difficult to solve for the time being:

[0004] 1. With the increasing demand for cryogenic cooling capacity in large scientific facilities, the current research and development frontier of 2K heat exchangers is kilowatt-class heat exchangers with large flow rates (>20g). However, actual testing of large-flow 2K heat exchangers under real working conditions is very difficult and extremely expensive. It is often necessary to complete the construction of a large cryogenic system before testing conditions are available. The construction and commissioning cycle of a large cryogenic system often takes several years, and the cost of startup and operation is as high as hundreds of thousands of yuan per day. This results in the supporting 2K heat exchangers often being idle for a long time after the completion of the preliminary design and manufacturing, lacking effective means to determine their actual performance, and unable to carry out further iterative optimization work.

[0005] 2. For 2K heat exchangers, judging from the few actual test results available, the performance indicators obtained from the preliminary design calculations often deviate greatly from the final test results. Sometimes, the design calculation pressure drop is 80Pa, while the actual measured pressure drop exceeds 200Pa. There is currently no good quantitative theoretical explanation for the source of this huge error, nor a specific correction method.

[0006] The 3.2K heat exchanger operates in an extremely low temperature environment. The working fluid flowing inside it is superfluid helium, a fluid with very extreme physical properties. Its flow and heat transfer dimensionless numbers, such as the Reynolds number, Prandtl number, and Nusselt number, are difficult to obtain using other conventional working fluids. Therefore, the "similar" experiments commonly used in fluid mechanics and heat transfer are also difficult to carry out. Summary of the invention

[0007] In view of the problems existing in the prior art, the purpose of the present invention is to provide a method for correcting the accuracy of the numerical model of a 2K ultra-low temperature heat exchanger using normal temperature test data. The present invention uses a cheap and convenient method to more accurately predict the actual performance of the 2K heat exchanger. This is an uncertainty quantification and uncertainty extrapolation technology, which will continue to play an important role in the future research and development of 2K heat exchangers.

[0008] The present invention adopts for the first time a data correction processing method and idea of ​​using a numerical model and experimental data under normal temperature conditions to correct experimental data under actual low temperature conditions; and provides a corresponding basis for data correction by analyzing multi-dimensional uncertainties.

[0009] The technical solution of the present invention is:

[0010] A method for correcting the accuracy of a 2K ultra-low temperature heat exchanger numerical model using normal temperature data, the steps comprising:

[0011] 1) The global sensitivity analysis Sobol method is used to determine the 2K ultra-low temperature heat exchanger input parameters that have the greatest impact on the output results of the 2K ultra-low temperature heat exchanger numerical model and divide them into two groups, namely, the input parameter vector P1 under normal temperature conditions and the input parameter vector P2 under low temperature conditions;

[0012] 2) Based on prior knowledge, the Gaussian distribution coefficient of each set of input parameters is obtained and the results of uncertainty propagation are analyzed. The Latin hypercube sampling method is used for simulation to obtain the uncertainty δ corresponding to the input parameter vector P1 in_1 and the uncertainty δ corresponding to the input parameter vector P2 in_2 ;

[0013] 3) Obtain experimental data through normal temperature experimental test, and analyze the experimental data to obtain the experimental uncertainty δ of the normal temperature test D_1 ;

[0014] 4) Through the formula The uncertainty of the numerical method under normal temperature conditions is calculated as follows: num_1 and the uncertainty of the numerical method under low temperature conditions δ num_2 ; δ iter is the iterative uncertainty of the numerical method under normal temperature conditions, δ discret is the discrete uncertainty of the numerical method under normal temperature conditions,

[0015] δ iter_max is the iteration uncertainty δ iter The maximum value of δ discret_max is the discrete uncertainty δ discret The maximum value of

[0016] 5) Through the formula δ model =-E+(δ D_1 -δ in_1 )-δ num_1 The model structure uncertainty δ of the 2K ultra-low temperature heat exchanger numerical model is calculated model ; Among them, the term E represents the deviation between the numerical simulation result S and the experimental value D;

[0017] 6) Using the model structural uncertainty δ model , combined with δ num_2 , δ in_2 Obtain the complete uncertainty of the numerical simulation value of the 2K ultra-low temperature heat exchanger numerical model under low temperature conditions;

[0018] 7) Correct the output results of the 2K ultra-low temperature heat exchanger numerical model according to the complete uncertainty.

[0019] Furthermore, the model structural uncertainty δ model As a probability box, a Markov chain Monte Carlo joint Bayesian method is constructed to use the results of room temperature testing to correct the model structural uncertainty δ model The posterior probability Among them, d(Y exp ,Y sim ) is the experimental data Y exp and the calculated result Y sim The error of σ represents the experimental data Y exp and the calculated result Y sim The standard deviation of the error between model , combined with δ num_2 , δ in_2 Obtain the complete uncertainty of the numerical simulation values ​​under low temperature conditions.

[0020] Furthermore, the experimental uncertainty δ is obtained D_1 The method is as follows: obtain a posteriori experimental data through normal temperature experimental test, then use the posteriori experimental data to obtain the parameters of the Gaussian distribution function used to describe the uncertainty of the boundary conditions of the 2K ultra-low temperature heat exchanger, and obtain the experimental uncertainty δ of the normal temperature test according to the mathematical expectation and variance of the Gaussian distribution function. D_1 .

[0021] Furthermore, the iteration uncertainty δ iter is the residual error of the first two steps before convergence.

[0022] Furthermore, the Richardson extrapolation method is used to construct discrete grids of different densities to obtain multiple sets of calculation results, and the discrete uncertainty δ is estimated based on the differences between the multiple sets of calculation results. discret .

[0023] The advantages of the present invention are as follows:

[0024] The present invention combines the methods of a priori modeling and a posteriori correction to quantify and correct the uncertainty of the 2K heat exchanger numerical model. The present invention can make full use of the 2K heat exchanger test data under non-standard operating conditions. When the real 2K low-temperature conditions cannot be obtained, the uncertainty of the numerical model can be effectively evaluated and corrected by conducting inexpensive normal temperature air tests, which greatly saves experimental costs and helps to quickly carry out structural iteration and performance research of the 2K heat exchanger. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Schematic diagram of 2K heat exchanger and its operation.

[0026] Figure 2 This is a diagram of uncertainty.

[0027] Figure 3 This is a comparison chart of the plans;

[0028] (a) Simplified diagram of the uncertainty correction process of the general model, (b) Simplified diagram of the uncertainty correction process of the present invention.

[0029] Figure 4 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0030] The present invention is further described in detail below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention but not to limit the scope of the present invention.

[0031] The present invention is an uncertainty quantification and uncertainty extrapolation technology. Generally speaking, uncertainty can be divided into two categories: random uncertainty and epistemic uncertainty. Random uncertainty is generally unavoidable, but it is easier to describe it using a probability function. Epistemic uncertainty stems from the one-sided understanding of things, and it is not easy to determine the specific probability function of such uncertainty. The core work of the entire uncertainty quantification and correction work is to determine the mathematical expression of various types of uncertainty and the specific parameter values.

[0032] For the numerical model in this scenario, its overall uncertainty includes many specific sources, which can be roughly divided into three categories: input parameter uncertainty (boundary conditions, physical parameters, etc.), model structure uncertainty (simplification of geometric structure, assumptions of physical phenomena, selection of turbulence model, etc.), and numerical method uncertainty (grid density, discrete error, numerical calculation method and parameters, etc.). At the same time, the experimental data itself also has certain uncertainties, such as Figure 2 The problem to be solved by the present invention is to evaluate these sub-item uncertainties in turn and correct them using experimental data from non-actual working conditions, such as Figure 3 As shown. Among them, input parameter uncertainty and experimental uncertainty belong to random uncertainty, which are generally represented by Gaussian distribution. Model structure uncertainty and numerical method uncertainty belong to epistemic uncertainty, which are described by probability box model (p-box) and uniform distribution model respectively in this invention.

[0033] (1) Input parameter uncertainty. For a 2K heat exchanger, the input parameters of its numerical model mainly include the following items: inlet boundary conditions (high-pressure side inlet temperature / pressure / flow and low-pressure side inlet temperature / pressure / flow), physical properties of the working fluid and heat exchanger materials, geometric parameters, etc. For the uncertainty of the output results caused by operating at normal temperature conditions and actual low-temperature conditions, the global sensitivity analysis Sobol method is first used to determine the parameters that have the greatest impact on the output results. According to the normal temperature conditions and low-temperature conditions, they are divided into two groups of parameter vectors, denoted as P1 and P2, respectively. Among them, P1 is the parameter vector under normal temperature conditions, and P2 is the parameter vector under low-temperature conditions. Then, based on prior knowledge, the Gaussian distribution coefficients of each group of input parameters are given and the results of uncertainty propagation are analyzed. The Latin hypercube sampling method is used for simulation, and finally the uncertainty δ corresponding to the input parameter vector P1 can be obtained. in_1 and the uncertainty δ corresponding to the input parameter vector P2 in_2 .

[0034] (2) Experimental uncertainty. The experimental test data of the 2K heat exchanger is actually the boundary conditions, including the measured values ​​of temperature, pressure and flow at the inlet and outlet. Therefore, its uncertainty is the Gaussian distribution function. The specific parameters of the Gaussian distribution function used to describe the uncertainty can be directly obtained through the a posteriori sampling measurement data. By calculating the mathematical expectation and variance of the data, the experimental uncertainty δ of the normal temperature test can be finally obtained. D_1 .

[0035] (3) Uncertainty of numerical method. The uncertainty of numerical method mainly comes from two sub-items: iteration and spatial discretization. It is assumed that the two uncertainties are independent of each other. In addition, there is no time term in the numerical model of 2K heat exchanger, so the time discretization error is not considered.

[0036]

[0037] Iterative uncertainty δ of the numerical method under normal temperature conditions iter It is expressed as the residual error of the first two steps before convergence, such as the outlet temperature, which is generally in the order of 1e-3. Discrete uncertainty δ discret The Richardson Extrapolation method is used to obtain several sets of calculation results by constructing discrete grids of different densities, and the specific value of the discrete uncertainty is estimated based on the difference between these results. The square average of the maximum values ​​of the two uncertainties is the uncertainty of the numerical method:

[0038]

[0039] Assuming that the uncertainty of the numerical method conforms to a uniform distribution, its distribution is [-δ num_max ,+δ num_max ]. Then according to the uncertainty calculation method, the uncertainty of the numerical method under normal temperature conditions is calculated as follows: num_1 and the uncertainty of the numerical method under low temperature conditions δ num_2 .

[0040] (4) Model structural uncertainty. Model structural uncertainty δ model There is a lot of cognitive uncertainty in it, so it is difficult to directly give it based on prior knowledge. Figure 2 It can be seen that the model structural uncertainty can be expressed using other uncertainties.

[0041] E=SD (3)

[0042] S+δ model +δ num +δ in =D+δ D (4)

[0043] δ model =-E+(δ D -δ in )-δ num (5)

[0044] The E term represents the deviation between the numerical simulation result S and the experimental value D, and the experimental uncertainty δ D With input uncertainty δ in The difference (δ D -δ in ) is a normal distribution with a mean of 0, and the uncertainty of the numerical method δ num is still a uniform distribution, so δ modelIt is a probability box (p-box) that can simultaneously describe mixed uncertainty of randomness and epistemicity.

[0045] Since the 3D geometric model and entity of the 2K heat exchanger used in the two working conditions are exactly the same, it is assumed that the δ model This is also the premise for the application of this method. In fact, since the sources of various errors are not completely independent, there will inevitably be a certain degree of coupling effect, but this low-order influence needs to be ignored first.

[0046] Construct a Markov chain Monte Carlo (MCMC) combined with a Bayesian method to use the results of the room temperature test to correct δ model The posterior probability P(θ|Y exp ), the main formula is:

[0047]

[0048] P(θ|Y exp ) is in Y exp The probability of the event θ occurring under the condition of the event occurring, P L (Y exp |θ) is Y under the condition that event θ occurs exp The probability of an event, Y exp Event refers to the uncertainty of the experimental data at room temperature, while θ event refers to the uncertainty of the simulation data at room temperature. L (Y exp |θ) Experimental data distribution is difficult to obtain and generally requires a very large sample. In the case of a small sample, the following formula is used to approximate it.

[0049]

[0050] d(Y exp ,Y sim ) is a function that characterizes the error between experimental data and calculation results, that is, E, Y in the previous formula exp The test results and Y sim is the simulation result. In the 2K heat exchanger working condition, we are mainly concerned with two variables, namely, outlet pressure and outlet temperature, which constitute a two-dimensional vector, represented by Bhattacharyya distance, where σ represents the standard deviation of the error between the experimental data and the calculation results. Initially, the arithmetic mean of E is taken as the initial value, and the initial δ model The probability box model is then continuously used to sample the posterior distribution and update the likelihood function using the Bayesian formula, and finally the posterior δ corrected by the experimental data can be obtained. model , the mathematical form is the probability box after parameter update.

[0051] Once the results of the normal temperature test are obtained, the posterior δ model After that, according to δ model and δ num_2 , δ in_2 , re-evaluate the complete uncertainty of the numerical simulation values ​​for the cryogenic conditions.

[0052] The overall implementation steps are as follows: Figure 4 As shown:

[0053] The whole process consists of four parts

[0054] In the first part, the global sensitivity analysis Sobol method is used to determine the parameters that have the greatest impact on the output results. The input parameter vectors are divided into two groups according to the normal temperature condition and the low temperature condition, which are recorded as P1 and P2 respectively. Then, the Gaussian parameter distribution coefficient of each group of input parameters is given according to the prior knowledge, and the uncertainty δ of the two groups of input parameters is obtained by the Latin hypercube sampling method. in_1 and δ in_2 In the second part, experimental data are obtained in the normal temperature test, and the experimental uncertainty δ of the normal temperature test is obtained by analyzing the experimental data. D_1 In the third part, the uncertainty of the numerical method under normal temperature conditions is calculated by formula (1) (2): num_1 and the uncertainty of the numerical method under low temperature conditions δ num_2 In the fourth part, after obtaining the above data, the posterior δ corrected by the experimental data is calculated by formula (3)(4)(5)(7) model , that is, the model structure uncertainty of the 2K ultra-low temperature heat exchanger numerical model.

[0055] After obtaining δ model After that, combined with δ num_2 , δ in_2 , re-evaluate the complete uncertainty of the numerical simulation value under low temperature conditions. Then, the output results of the 2K ultra-low temperature heat exchanger numerical model are corrected according to the final complete uncertainty, and the degree of correction depends on the final difference.

[0056] Although the specific embodiments of the present invention are disclosed for the purpose of illustration, the purpose is to help understand the content of the present invention and implement it accordingly, those skilled in the art will understand that various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the best embodiment, and the scope of the present invention is subject to the scope defined in the claims.

Claims

1. A method for correcting the accuracy of a 2K ultra-low temperature heat exchanger numerical model using normal temperature data, the steps comprising: 1) The global sensitivity analysis Sobol method is used to determine the 2K ultra-low temperature heat exchanger input parameters that have the greatest impact on the output results of the 2K ultra-low temperature heat exchanger numerical model and divide them into two groups, namely, the input parameter vector P1 under normal temperature conditions and the input parameter vector P2 under low temperature conditions; 2) Based on prior knowledge, the Gaussian distribution coefficient of each set of input parameters is obtained and the results of uncertainty propagation are analyzed. The Latin hypercube sampling method is used for simulation to obtain the uncertainty δ corresponding to the input parameter vector P1 in_1 and the uncertainty δ corresponding to the input parameter vector P2 in_2 ; 3) Obtain experimental data through normal temperature experimental test, and analyze the experimental data to obtain the experimental uncertainty δ of the normal temperature test D_1 ; 4) Through the formula The uncertainty of the numerical method under normal temperature conditions is calculated as follows: num_1 and the uncertainty of the numerical method under low temperature conditions δ num_2 ; δ iter is the iterative uncertainty of the numerical method under normal temperature conditions, δ discret is the discrete uncertainty of the numerical method under normal temperature conditions, δ iter_max is the iteration uncertainty δ iter The maximum value of δ discret_max is the discrete uncertainty δ discret The maximum value of 5) Through the formula δ model =-E+(δ D_1 -δ in_1 )-δ num_1 The model structure uncertainty δ of the 2K ultra-low temperature heat exchanger numerical model is calculated model ; Among them, the term E represents the deviation between the numerical simulation result S and the experimental value D; 6) Using the model structural uncertainty δ model , combined with δ num_2 , δ in_2 Obtain the complete uncertainty of the numerical simulation value of the 2K ultra-low temperature heat exchanger numerical model under low temperature conditions; 7) Correct the output results of the 2K ultra-low temperature heat exchanger numerical model according to the complete uncertainty.

2. The method according to claim 1, characterized in that: The model structural uncertainty δ model As a probability box, a Markov chain Monte Carlo joint Bayesian method is constructed to use the results of room temperature testing to correct the model structural uncertainty δ model The posterior probability Among them, d(Y exp , Y sim ) is the experimental data Y exp and the calculated result Y sim The error of σ represents the experimental data Y exp and the calculated result Y sim The standard deviation of the error between model , combined with δ num_2 , δ in_2 Obtain the complete uncertainty of the numerical simulation values ​​under low temperature conditions.

3. The method according to claim 1, characterized in that The experimental uncertainty δ is obtained D_1 The method is as follows: obtain a posteriori experimental data through normal temperature experimental test, then use the posteriori experimental data to obtain the parameters of the Gaussian distribution function used to describe the uncertainty of the boundary conditions of the 2K ultra-low temperature heat exchanger, and obtain the experimental uncertainty δ of the normal temperature test according to the mathematical expectation and variance of the Gaussian distribution function. D_1 .

4. The method according to claim 1, 2 or 3, characterized in that: The iteration uncertainty δ iter is the residual error of the first two steps before convergence.

5. The method according to claim 1, 2 or 3, characterized in that: The Richardson extrapolation method is used to construct discrete grids of different densities to obtain multiple sets of calculation results, and the discrete uncertainty δ is estimated based on the differences between the multiple sets of calculation results. discret .

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