Method for determining the mixing coefficient of fuel assemblies

Abstract

An embodiment of the present invention relates to the field of thermal analysis or optimization technology, and specifically to a method for determining the mixing coefficient of a fuel assembly, comprising: S1, simulating the fuel assembly; S2, determining multiple estimated values ​​of the mixing coefficient based on the structure and operating parameters of the simulated fuel assembly; S3, measuring multiple test points of each channel of the set simulated fuel assembly to obtain temperature measurement values ​​of the multiple test points; S4, determining the temperature calculation values ​​of the multiple test points based on each estimated value; S5, determining the error between the temperature calculation value and the temperature measurement value based on the temperature calculation value and the temperature measurement value; S6, calculating the difference between the temperature calculation values ​​of the test points of each channel corresponding to multiple estimated values ​​of different mixing coefficients to determine the maximum temperature difference; S7, fitting the error and the maximum temperature difference into a first predetermined function; S8, fitting the mixing coefficient and the maximum temperature difference into a second predetermined function; S9, determining the mixing coefficient of the fuel assembly based on the maximum temperature difference.

Description

Technical Field

[0001] Embodiments of the present invention relate to the technical field of thermal analysis or optimization, and in particular to a method for determining a mixing coefficient of a fuel assembly. Background Art

[0002] The statements herein merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] The mixing performance between the channels of the fuel assembly is an important research topic in the thermal-hydraulic performance of the core. Superior mixing performance can greatly improve the thermal-hydraulic performance of the core fuel assembly. The parameter used to characterize the mixing performance is the mixing coefficient, which is generally obtained through experimental measurements.

[0004] In the currently commonly used experimental measurement method, the temperature distribution of each channel of the fuel assembly can only be measured, the sum of squared errors can be determined based on the temperature distribution of each channel, and the curve of the sum of squared errors changing with the mixing coefficient can be directly observed. Finally, the mixing coefficient corresponding to the minimum value of the sum of squared errors is selected as the approximate solution. However, due to the complex variation pattern of the sum of squared errors and the mixing coefficient and the lack of an accurate fitting method, the accurate minimum value of the sum of squared errors cannot be obtained. Therefore, in order to improve the calculation accuracy of the mixing coefficient, multiple iterations can only be performed, and the calculation process is complicated, tedious and inefficient. Summary of the Invention

[0005] A brief overview of the present application is provided below to provide a basic understanding of certain aspects of the present application. It should be understood that this overview is not an exhaustive overview of the present application. It is not intended to identify key or important portions of the present application, nor is it intended to limit the scope of the present application. Its purpose is simply to present certain concepts in a simplified form as a prelude to the more detailed description that will be discussed later.

[0006] An embodiment of the present invention provides a method for determining the mixing coefficient of a fuel assembly, the method comprising the following steps: S1, simulating the fuel assembly; S2, determining multiple estimated values ​​of the mixing coefficient based on the structure and operating parameters of the simulated fuel assembly; S3, measuring multiple test points of each channel of the set simulated fuel assembly to obtain temperature measurement values ​​of the multiple test points; S4, determining the temperature calculation values ​​of the multiple test points based on each estimated value; S5, determining the error between the temperature calculation value and the temperature measurement value based on the temperature calculation value and the temperature measurement value; S6, calculating the difference between the temperature calculation values ​​of the test points of each channel corresponding to multiple estimated values ​​of different mixing coefficients to determine the maximum temperature difference; S7, fitting the error and the maximum temperature difference into a first predetermined function; S8, fitting the mixing coefficient and the maximum temperature difference into a second predetermined function; S9, determining the mixing coefficient of the fuel assembly based on the maximum temperature difference.

[0007] The method in the embodiment of the present invention determines the error between the temperature calculation value and the measured value of multiple test points of each channel, and the maximum value of the difference between the calculated values ​​of the test points of each channel corresponding to multiple estimated values ​​of different mixing coefficients, that is, the maximum temperature difference, and fits the error and the maximum temperature difference, as well as the mixing coefficient and the maximum temperature difference, respectively. The fitting accuracy is high, so as to accurately obtain the change pattern of the error with the maximum temperature difference, and the change pattern of the maximum temperature difference with the mixing coefficient, thereby improving the accuracy of the finally determined mixing coefficient, while simplifying the determination process of the mixing coefficient, reducing the amount of calculation, and improving efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Other objects and advantages of the present invention will become apparent from the following description of the embodiments of the present invention with reference to the accompanying drawings, which will help to provide a comprehensive understanding of the present invention.

[0009] Figure 1 is a flow chart of a method for determining a mixing coefficient of a fuel assembly according to one embodiment of the present invention.

[0010] Figure 2 FIG. 4 is a curve showing a change in error with the maximum temperature difference according to an embodiment of the present invention.

[0011] Figure 3 is a curve showing how the mixing coefficient changes with the maximum temperature difference according to one embodiment of the present invention.

[0012] It should be noted that the drawings are not necessarily drawn to scale, but are merely shown in a schematic manner that does not affect the reader's understanding. DETAILED DESCRIPTION

[0013] Exemplary embodiments of the present invention are described below with reference to the accompanying drawings. For the sake of clarity and conciseness, not all features of an actual implementation are described in this specification. However, it should be understood that in the process of developing any such actual implementation, many implementation-specific decisions must be made in order to achieve the developer's specific goals, such as meeting those constraints related to the system and business, and these constraints may vary from implementation to implementation. In addition, it should be understood that although the development work may be very complex and time-consuming, it is a routine task for those skilled in the art who benefit from the disclosure of this application.

[0014] It is also necessary to explain here that, in order to avoid obscuring the present invention due to unnecessary details, the accompanying drawings only show the device structure and / or processing steps that are closely related to the solution according to the present invention, while other details that are not closely related to the present invention are omitted.

[0015] An embodiment of the present invention provides a method for determining the mixing coefficient of a fuel assembly, such as Figure 1 As shown, the method includes the following steps S1 to S9.

[0016] S1: Simulate the fuel assembly.

[0017] S2: Determine multiple estimated values ​​of the mixing coefficient based on the structure and operating parameters of the simulated fuel assembly.

[0018] S3: measuring a plurality of test points of each channel of the simulated fuel assembly to obtain temperature measurement values ​​of the plurality of test points.

[0019] S4: Based on each estimated value, determine temperature calculation values ​​of the plurality of test points.

[0020] S5: Determine an error between the calculated temperature value and the measured temperature value according to the calculated temperature value and the measured temperature value.

[0021] S6: Calculate the difference between the temperature calculation values ​​of the test points of each channel corresponding to multiple estimated values ​​of different mixing coefficients to determine the maximum temperature difference.

[0022] S7: Fitting the error and the maximum temperature difference into a first predetermined function.

[0023] S8: Fitting the mixing coefficient and the maximum temperature difference into a second predetermined function.

[0024] S9: Determine the mixing coefficient of the fuel assembly based on the maximum temperature difference.

[0025] The method provided by an embodiment of the present invention determines the error between the temperature calculation value and the measured value of multiple test points of each channel, as well as the maximum value of the difference between the calculated values ​​of the test points of each channel corresponding to multiple estimated values ​​of different mixing coefficients, that is, the maximum temperature difference, and fits the error and the maximum temperature difference, as well as the mixing coefficient and the maximum temperature difference, respectively. The fitting accuracy is high, so as to accurately obtain the variation pattern of the error with the maximum temperature difference, and the variation pattern of the maximum temperature difference with the mixing coefficient, thereby improving the accuracy of the finally determined mixing coefficient, while simplifying the determination process of the mixing coefficient, reducing the amount of calculation, and improving efficiency.

[0026] In some embodiments, in step S2, when determining multiple estimated values ​​of the mixing coefficient, multiple different values ​​of the mixing coefficient can be selected within the range that the mixing coefficient may fall into based on the structure and operating parameters of the simulated fuel assembly and experience, as multiple estimated values ​​of the mixing coefficient.

[0027] In some embodiments, in step S3, a test point may be set in each channel of the simulated fuel assembly to obtain multiple test points in each channel, and then the temperatures of the multiple test points are measured to obtain temperature measurement values ​​of the multiple test points.

[0028] In some embodiments, step S4 may further include: S41, determining the temperature distribution of each channel corresponding to each estimated value of the mixing coefficient based on each estimated value of the mixing coefficient; S42, determining the temperature calculation values ​​of multiple test points of each channel according to the temperature distribution of each channel.

[0029] Specifically, in step S41, each channel of the simulated fuel assembly may be modeled one by one, and the temperature distribution of each channel may be obtained through numerical solution.

[0030] In some embodiments, in step S5, the error between the calculated temperature value and the measured temperature value satisfies the following relationship:

[0031]

[0032] Where s represents the error and m represents the number of subchannels. The temperature measurement value of the i-th subchannel is T ai , the calculated temperature is T pi , the temperature measurement value of the jth sub-channel is T aj , the calculated temperature is T pj In this way, the error between the calculated temperature value and the measured temperature value at multiple test points of the simulated fuel assembly is obtained.

[0033] In some embodiments, in step S6, the differences between the temperature calculation values ​​of the test points of each channel corresponding to multiple estimated values ​​of different mixing coefficients may be calculated respectively, and the maximum value of the differences between the temperature calculation values ​​is determined as the maximum temperature difference.

[0034] In some embodiments, in step S7, the first predetermined function is the following relationship:

[0035]

[0036] s represents the error, T β represents the maximum temperature difference, and A1, B1, and C1 are constants. The relationship between the error and the maximum temperature difference can be accurately fitted using this equation to obtain the changing relationship between the error and the maximum temperature difference.

[0037] In some embodiments, the relationship of the first predetermined function is determined as follows: Since the temperature measurement value of the i-th sub-channel of the simulated fuel assembly is T ai , and the temperature measurement value of the jth subchannel is T ajis a fixed constant, and the error s is a function of the calculated temperature values ​​at multiple test points on the simulated fuel assembly. Furthermore, for the same simulated fuel assembly, the ratio of the differences between the calculated temperature values ​​at the test points in each channel corresponding to multiple estimated values ​​of the mixing coefficient is a constant value that varies very little with the mixing coefficient. Therefore, the ratio of the differences between the calculated temperature values ​​can be approximated as a constant.

[0038] Therefore, the difference T between the calculated temperature values ​​in formula (1) is pi -T pj You can use k ij T β Substituting into formula (1) we get:

[0039]

[0040] Where kij is the difference between the calculated temperature values ​​of the ith subchannel and the jth subchannel and the maximum temperature difference T β The ratio of is a constant. Therefore, the error s is the maximum temperature difference T β Therefore, the error and the maximum temperature difference are fitted into a quadratic function according to formula (2).

[0041] In some embodiments, A1, B1, and C1 are determined by fitting to improve the fitting accuracy of the error and the maximum temperature difference and accurately reflect the variation of the error with the maximum temperature difference.

[0042] In some embodiments, in step S8, the second predetermined function satisfies the following expression:

[0043]

[0044] Where β represents the mixing coefficient, and A2, B2, and C2 are constants. This relationship can be used to accurately fit the maximum temperature difference to the mixing coefficient, yielding the relationship between the maximum temperature difference and the mixing coefficient.

[0045] In some embodiments, the expression of the second predetermined function is determined based on the following: since the difference between the calculated temperature values ​​of multiple test points in each channel decreases as the mixing coefficient increases, but when the mixing coefficient is 0, the difference between the calculated temperature values ​​is a certain value and does not tend to positive infinity, the maximum temperature difference is not inversely proportional to the mixing coefficient, and therefore an exponential decay law is assumed; however, when the mixing coefficient tends to positive infinity, the difference between the calculated temperature values ​​of multiple test points in each channel tends to a certain value and is not completely equal, so a constant term is assumed. Therefore, the maximum temperature difference and the mixing coefficient are fitted to the sum of an exponential function and a constant term according to formula (3).

[0046] Specifically, in step S8, when the mixing coefficient and the maximum temperature difference are fitted into the second predetermined function, the equation (3) can be transformed into the following expression by shifting the terms and taking the logarithm:

[0047] ln(T β -C2)=lnA2-B2β (4)

[0048] According to formula (4), first assume a value of C2, and then set ln(T β -C2) is linearly fitted with β and the fitting error R is calculated. 2 , and then adjust the value of C2 according to the fitting error, so that the fitting error R 2 Reaching the minimum, even if R 2 Close to 1, the value of C2 at this time is the fitting of C2. The slope of the straight line obtained by linear fitting is -B2, and the intercept is lnA2.

[0049] In some embodiments, A2, B2, and C2 are determined by fitting to improve the fitting accuracy of the maximum temperature difference and the mixing coefficient, and accurately reflect the variation of the maximum temperature difference with the mixing coefficient.

[0050] In some embodiments, in step S9, when s takes the minimum value, the maximum temperature difference is determined using the first predetermined function, and the mixing coefficient of the fuel assembly is determined based on the maximum temperature difference and the second predetermined function. The mixing coefficient of the fuel assembly is determined by utilizing the variation pattern of the error obtained by fitting with the maximum temperature difference, and the variation pattern of the maximum temperature difference with the mixing coefficient, thereby avoiding multiple trial calculations and iterations and reducing tedious and complicated workload.

[0051] In some embodiments, in step S9, when the maximum temperature difference is determined using the first predetermined function, the maximum temperature difference T when s takes the minimum value can be obtained based on the properties of the quadratic function and the fitting coefficients A1, B1, and C1. β The value of is as follows:

[0052]

[0053] In some embodiments, in step S9, when determining the mixing coefficient of the fuel assembly based on the maximum temperature difference and the second predetermined function, the expression of the mixing coefficient β can be first obtained by inversely solving equation (3), as shown below:

[0054]

[0055] Then, the maximum temperature difference T when s takes the minimum value determined by the first predetermined function is used. β Substituting into formula (6), the mixing coefficient β is calculated.

[0056] In some embodiments, based on the structure and operating parameters of the simulated fuel assembly, no fewer than five estimated values ​​of the mixing coefficient are determined to ensure fitting accuracy, thereby ensuring the accuracy of the ultimately determined mixing coefficient.

[0057] The following is a specific example to further illustrate the process of determining the mixing coefficient of a fuel assembly using the method of the present invention.

[0058] Example 1

[0059] First, the fuel assembly is simulated.

[0060] Second, based on the structure and operating parameters of the simulated fuel assembly, we empirically determined that within the possible range of the mixing coefficient, six values ​​of 0.006, 0.01, 0.014, 0.018, 0.022, and 0.026 were selected as multiple estimated values ​​of the mixing coefficient.

[0061] Third, multiple test points of each channel of the simulated fuel assembly are measured to obtain temperature measurement values ​​of the multiple test points.

[0062] Fourth, based on each estimated value of the mixing coefficient, the temperature distribution of each channel corresponding to each estimated value of the mixing coefficient is determined; and according to the temperature distribution, the temperature calculation values ​​of multiple test points of each channel are determined.

[0063] Fifth, based on the temperature calculation value and the temperature measurement value, the error between the temperature calculation value and the temperature measurement value is determined using formula (1).

[0064] Sixth, the difference between the temperature calculation values ​​of the test points of each channel corresponding to the multiple estimated values ​​of different mixing coefficients is calculated, and the maximum value of the temperature calculation values ​​is determined as the maximum temperature difference.

[0065] Seventh, compare the error s with the maximum temperature difference T β Specifically, according to formula (2), the error s and the maximum temperature difference T are obtained. β The changing relationship is as follows:

[0066]

[0067] Among them, the fitting error R 2 =0.9997. According to the change relationship, the error s is obtained as the maximum temperature difference T β The change curve of Figure 2 shown.

[0068] Eighth, the mixing coefficient β and the maximum temperature difference T β According to formula (3), the second predetermined function is fitted to obtain the mixing coefficient β and the maximum temperature difference T β The relationship between the mixing coefficient β and the maximum temperature difference T is obtained based on the relationship between the mixing coefficient β and the maximum temperature difference T. β The change curve of Figure 3 shown.

[0069] Ninth, according to the fitting coefficients 35.118 and -377.32, it is calculated according to formula (5) that when s takes the minimum value, the maximum temperature difference T β is 5.372℃; and then substituting it into formula (6), the mixing coefficient β of the fuel assembly is calculated to be 0.01694.

[0070] Regarding the embodiments of the present invention, it should also be noted that, in the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other to obtain new embodiments.

[0071] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for determining the mixing coefficient of a fuel assembly, characterized in that: It includes the following steps: S1: Simulate the fuel assembly. S2: determining a plurality of estimated values ​​of the mixing coefficient according to the structure and operating parameters of the simulated fuel assembly; S3: measuring a plurality of test points of each channel of the simulated fuel assembly to obtain temperature measurement values ​​of the plurality of test points; S4: determining calculated temperature values ​​of the plurality of test points based on each estimated value; S5: determining an error between the calculated temperature value and the measured temperature value according to the calculated temperature value and the measured temperature value; S6: Calculating the difference between the temperature calculation values ​​of the test points of each channel corresponding to the multiple estimated values ​​of different mixing coefficients to determine the maximum temperature difference; S7: fitting the error and the maximum temperature difference into a first predetermined function; S8: fitting the mixing coefficient and the maximum temperature difference into a second predetermined function; S9: Determining a mixing coefficient of the fuel assembly according to the maximum temperature difference; In step S7, the first predetermined function is the following relational expression: ， s represents the error, T β Indicates the maximum temperature difference, A1, B1, C1 are constants; In step S8, the second predetermined function satisfies the following expression: ， Among them, T β represents the maximum temperature difference, β represents the mixing coefficient, A2, B2, C2 are constants; In step S9, when s takes the minimum value, the maximum temperature difference is determined using the first predetermined function. A mixing coefficient of the fuel assembly is determined according to the maximum temperature difference and the second predetermined function.

2. The method according to claim 1, characterized in that In step S5, the error satisfies the following relationship: ， Where s represents the error, m represents the number of subchannels, and the temperature measurement value of the i-th subchannel is T ai , the calculated temperature is T pi , the temperature measurement value of the jth sub-channel is T aj , the calculated temperature is T pj .

3. The method according to claim 1, characterized in that The A1, B1, and C1 are determined by fitting.

4. The method according to claim 1, wherein The A2, B2, and C2 are determined by fitting.

5. The method according to claim 1, wherein The plurality of estimated values ​​is no less than 5.

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