Method for correcting accuracy of numerical model of 2K ultra-low temperature heat exchanger by using normal temperature data

Abstract

The present invention discloses a method for correcting the accuracy of a numerical model of a 2K ultra-low temperature heat exchanger by using normal temperature data. The steps include: 1) using the Sobol method to determine the input parameter vectors P1 under normal temperature conditions and P2 under low temperature conditions that have the greatest influence on the output results; 2) obtaining the uncertainty δin_1 corresponding to P1 and the uncertainty δin_2 corresponding to P2 according to prior knowledge; 3) obtaining the experimental uncertainty δD_1 of normal temperature testing; 4) calculating the numerical method uncertainties δnum_1 and δnum_2 under normal temperature conditions and low temperature conditions; 5) calculating the model structure uncertainty δmodel; 6) using the model structure uncertainty δmodel, combining δnum_2 and δin_2 to obtain the complete uncertainty of the numerical simulation value under low temperature conditions; 7) correcting the output results of the numerical model of the 2K ultra-low temperature heat exchanger according to the complete uncertainty.

Description

Technical Field

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

[0002] The 2K helium cryogenic system is responsible for providing an ultra-low temperature environment for large scientific installations such as large superconducting accelerators / large superconducting fusion reactors. As shown in Figure 1 the figure, the 2K superfluid helium cryogenic heat exchanger (hereinafter referred to as the 2K heat exchanger) 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 and is responsible for recovering the cold energy of the 2K helium vapor and increasing the liquid outlet rate of the last-stage throttle valve. The heat transfer efficiency and the pressure drop on the low-pressure side of the 2K heat exchanger are two core performance indicators, which directly affect the liquid outlet rate and the load of the rotating machinery on the low-pressure side.

[0003] At present, some research work has been carried out on the 2K heat exchanger, and research has been carried out on the 2K heat exchanger from aspects such as design, optimization, manufacturing, and testing. However, there are still several problems that are difficult to solve temporarily:

[0004] 1. With the continuous increase in the demand for cryogenic cold energy in large scientific installations, the current R & D frontier of the 2K heat exchanger is a kilowatt-level heat exchanger with a large flow rate (>20 g). However, the actual test of the real working conditions of the 2K heat exchanger with a large flow rate is very difficult and extremely costly. It is often necessary to have the test conditions only after the entire set of large cryogenic systems is completely built. The construction and commissioning cycle of large cryogenic systems often lasts for several years, and the cost during startup operation is also 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 preliminary design and manufacturing are completed, lacking effective means to determine their actual performance, and also unable to carry out further iterative optimization work.

[0005] 2. For the 2K heat exchanger, judging from the small amount of actual test results available at present, the performance indicators obtained from the preliminary design calculations often deviate greatly from the final test results. Sometimes, there is even a situation where the designed calculated pressure drop is 80 Pa, while the actually measured pressure drop exceeds 200 Pa. At present, there is no good quantitative theoretical explanation for the source of this huge error, nor is there a specific correction method given.

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

[0007] Aiming at the problems existing in the prior art, the purpose of the present invention is to provide a method for correcting the numerical model accuracy of a 2K ultra-low temperature heat exchanger by using room temperature test data. The present invention conducts a more accurate prediction of the true performance of the 2K heat exchanger through an inexpensive and convenient method, which is an uncertainty quantification and uncertainty extrapolation technology and will continue to play an important role in the future research and development process of the 2K heat exchanger.

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

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

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

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

[0012] 2) Obtain the Gaussian distribution coefficients of each group of input parameters according to prior knowledge and analyze the results of uncertainty propagation, and use the Latin hypercube sampling method for simulation to obtain the uncertainty δ in_1 corresponding to the input parameter vector P1 and the uncertainty δ in_2 corresponding to the input parameter vector P2;

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

[0014] 4) Calculate to obtain the numerical method uncertainty δ under room temperature conditions and the numerical method uncertainty δ num_1 under low temperature conditions and δ num_2 ; δ iter is the iterative uncertainty of the numerical method under room temperature conditions, and δ discret is the discrete uncertainty of the numerical method under room temperature conditions,

[0015] δ iter_max is the maximum value of the iterative uncertainty δ iter ; δ discret_max is the maximum value of the discrete uncertainty δ discret ;

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

[0017] 6) Use the model structure uncertainty δ model , combined with δ num_2 , δ in_2 to 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 result of the 2K ultra-low temperature heat exchanger numerical model according to the said complete uncertainty.

[0019] Furthermore, the model structure uncertainty δ model is a probability box, and a Markov chain Monte Carlo joint Bayesian method is constructed to use the results of room temperature tests to correct the posterior probability of the model structure uncertainty δ model ; where d(Y ,Y exp ,Y sim ) represents the error between the experimental data Y exp and the calculation result Y sim , and σ represents the standard deviation of the error between the experimental data Y exp and the calculation result Y sim ; then use the corrected model structure uncertainty δ model , combined with δ num_2 , δ in_2 to obtain the complete uncertainty of the numerical simulation value under low temperature conditions.

[0020] Furthermore, the method for obtaining the experimental uncertainty δ D_1 is: obtain the posterior experimental data through room temperature experimental tests, then use the posterior 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 D_1 of the room temperature test according to the mathematical expectation and variance of the Gaussian distribution function.

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

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

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

[0024] The present invention combines the methods of prior modeling and posterior correction to quantify and correct the uncertainty of the 2K heat exchanger numerical model. Using the present invention, the test data of the 2K heat exchanger under non-standard working conditions can be fully utilized. When the true 2K low-temperature working conditions cannot be obtained, by conducting inexpensive normal-temperature air tests, the uncertainty of the numerical model can also be effectively evaluated and corrected, greatly saving the experimental cost, and helping to quickly carry out the structure iteration and performance research work of the 2K heat exchanger. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a schematic diagram of the 2K heat exchanger and its operation.

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

[0027] Figure 3 is a comparison diagram of the schemes;

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

[0029] Figure 4 is a flow chart of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] The present invention will be further described in detail below with reference to the drawings. The examples given are only used to explain the present invention and are not intended 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 relatively easy to describe using probability functions. Epistemic uncertainty, on the other hand, stems from the one-sidedness of the 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 forms and specific parameter values of various uncertainties.

[0032] For the numerical model in this scenario, its overall uncertainty contains many specific sources, which can generally be divided into three categories: input parameter uncertainty (boundary conditions, physical property parameters, etc.), model structure uncertainty (simplification of geometric structure, assumptions of physical phenomena, selection of turbulence models, etc.), and numerical method uncertainty (mesh density, discretization error, numerical calculation methods and parameters, etc.). At the same time, the experimental data itself also has a certain degree of uncertainty, such as Figure 2 shown. The problem to be solved by the present invention is to evaluate these sub-uncertainties in turn and use experimental data under non-actual working conditions for correction, as Figure 3 shown. Among them, the input parameter uncertainty and experimental uncertainty belong to random uncertainties, and generally the Gaussian distribution is used to represent them. While the model structure uncertainty and numerical method uncertainty belong to epistemic uncertainties, and in the present invention, the probability box model (p-box) and uniform distribution model are used to describe them respectively.

[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 rate and low-pressure side inlet temperature / pressure / flow rate), physical property parameters of the working fluid and heat exchanger materials, geometric parameters, etc. For the uncertainties in the output results under normal temperature conditions and real low-temperature conditions, first use the global sensitivity analysis Sobol method to determine several parameters that have the greatest impact on the output results, and divide them into two groups of parameter vectors according to normal temperature conditions and low-temperature conditions, 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, according to prior knowledge, give the Gaussian distribution coefficients of each group of input parameters and analyze the results of uncertainty propagation, and use the Latin hypercube sampling method for simulation. Finally, the uncertainty δ in_1 corresponding to the input parameter vector P1 and the uncertainty δ in_2 corresponding to the input parameter vector P2 can be obtained respectively.

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

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

[0036]

[0037] Iterative uncertainty δ of the numerical method under normal temperature conditions iter It is expressed by the residuals of the first two steps before convergence. For example, the outlet temperature is generally on the order of 1e-3. Discretization uncertainty δ discret Then the Richardson extrapolation method is adopted. By constructing discrete grids with different densities, several sets of calculation results are obtained, and the specific value of the discretization uncertainty is estimated based on the differences between these results. The root mean square 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 follows a uniform distribution, its distribution is [-δ num_max , +δ num_max . Then, according to the uncertainty calculation method, the uncertainty δ of the numerical method under normal temperature conditions is calculated num_1 and the uncertainty δ of the numerical method under low temperature conditions num_2 .

[0040] (4) Model structure uncertainty. The model structure uncertainty δ model includes a large amount of epistemic uncertainty, so it is difficult to directly give it based on prior knowledge. However, according to Figure 2 it can be seen that the model structure uncertainty can be expressed using other uncertainties. It is expressed as follows

[0041] E = S - D (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 term E represents the deviation between the numerical simulation result S and the experimental value D. The difference between the experimental uncertainty δ D and the input uncertainty δ in . The term (δ D - δ in ) is a normal distribution with a mean of 0. The uncertainty δ of the numerical method num is still a uniform distribution. Therefore, δ modelIt is a probability box (p-box) that can simultaneously describe the mixed uncertainty of randomness and cognition.

[0045] Since the 3D geometric models and entities of the 2K heat exchanger used in the two working conditions are exactly the same, it is assumed that δ model is also the same, which is the prerequisite 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 effect needs to be ignored first.

[0046] Construct a Markov chain Monte Carlo (MCMC) joint Bayesian method to use the results of normal temperature tests to correct the posterior probability P(θ|Y model ) of δ exp . The main formula is:

[0047]

[0048] P(θ|Y exp ) is the probability of the occurrence of event θ under the condition that event Y exp occurs. P L (Y exp |θ) is the probability of the occurrence of event Y exp under the condition that event θ occurs. Event Y exp refers to the uncertainty of the obtained normal temperature experimental data, where event θ refers to the uncertainty of the normal temperature simulation data. And the explicit P 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 for approximation.

[0049]

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

[0051] Once the posterior δ is obtained from the results of the normal temperature test model then, according to δ model and δ num_2 , δ in_2 , re-evaluate the complete uncertainty of the numerical simulation values under the low temperature condition.

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

[0053] The whole process includes four parts

[0054] The first part is to use the global sensitivity analysis Sobol method to determine several parameters that have the greatest impact on the output results. According to the normal temperature condition and the low temperature condition, they are divided into two groups of input parameter vectors, denoted as P1 and P2 respectively. Then, according to prior knowledge, the Gaussian parameter distribution coefficients of each group of input parameters are given, and the Latin hypercube sampling method is used to obtain the uncertainties δ in_1 and δ in_2 . The second part is to obtain experimental data in the normal temperature experiment test, and analyze the experimental data to obtain the experimental uncertainty δ D_1 of the normal temperature test. The third part is to calculate the numerical method uncertainty δ num_1 under the normal temperature condition and the numerical method uncertainty δ num_2 under the low temperature condition through formulas (1) and (2). The fourth part is to calculate the posterior δ model corrected by using the experimental data through formulas (3), (4), (5), and (7), that is, the model structure uncertainty of the 2K ultra-low temperature heat exchanger numerical model.

[0055] After obtaining δ model , combined with δ num_2 , δ in_2 , re-evaluate the complete uncertainty of the numerical simulation values under the low temperature condition. Then, according to the finally obtained complete uncertainty, correct the output results of the 2K ultra-low temperature heat exchanger numerical model, and the degree of correction depends on the size of the final difference.

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

Claims

1. A method for correcting the accuracy of a numerical model of a 2K ultra-low temperature heat exchanger using ambient temperature data, the steps of which include: 1) Using the global sensitivity analysis Sobol method to determine a number of input parameters of the 2K ultra-low temperature heat exchanger that have the greatest impact on the output result of the numerical model of the 2K ultra-low temperature heat exchanger and dividing them into two groups, namely the input parameter vector P1 under ambient temperature conditions and the input parameter vector P2 under low temperature conditions; 2) Obtain the Gaussian distribution coefficients of each group of input parameters according to prior knowledge and analyze the results of uncertainty propagation. Use the Latin hypercube sampling method 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 room temperature experiments, and analyze the experimental data to obtain the experimental uncertainty δ of room temperature tests D_1 ; 4) Calculate the uncertainty δ of the numerical method under normal temperature conditions through the formula and the uncertainty δ of the numerical method under low temperature conditions num_1 ; δ num_2 is the iterative uncertainty of the numerical method under normal temperature conditions, and δ iter is the discretization uncertainty of the numerical method under normal temperature conditions. δ discret is the maximum value of the iterative uncertainty δ iter_max , and δ iter is the maximum value of the discretization uncertainty δ discret_max discret ;​ 5) Calculate the model structure uncertainty δ of the 2K ultra-low temperature heat exchanger numerical model through the formula δ model =-E+(δ D_1 -δ in_1 )-δ num_1 ; where the E term represents the deviation between the numerical simulation result S and the experimental value D; model ​ 6) Utilize the model structure uncertainty δ model , in combination with δ num_2 , δ in_2 to obtain the complete uncertainty of the numerical simulation value of the 2K ultra-low temperature heat exchanger numerical model under low temperature conditions; 7) Correcting the output result of the numerical model of the 2K ultra-low temperature heat exchanger according to the complete uncertainty.

2. The method according to claim 1, characterized in that, The model structure uncertainty δ model is a probability box, and a Markov chain Monte Carlo joint Bayesian method is constructed to use the results of normal temperature tests to correct the posterior probability of the model structure uncertainty δ model . Among them, d(Y exp , Y sim ) represents the error between the experimental data Y exp and the calculation result Y sim , σ represents the standard deviation of the error between the experimental data Y exp and the calculation result Y sim ; then the corrected model structure uncertainty δ model is used, combined with δ num_2 , δ in_2 to obtain the complete uncertainty of the numerical simulation value under low temperature conditions.

3. The method according to claim 1, wherein Obtain the experimental uncertainty δ D_1 The method is as follows: Obtain the posterior experimental data through room temperature experiment tests, then use the posterior 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 room temperature test according to the mathematical expectation and variance of the Gaussian distribution function D_1 .

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

5. The method according to claim 1 or 2 or 3, characterized in that The Richardson extrapolation method is used to construct discrete grids with 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 obtained calculation results. discret .

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