A method for evaluating keff uncertainty caused by nuclear cross section

Abstract

The present invention relates to a method for evaluating the uncertainty of keff caused by nuclear cross section deviation, belonging to the technical field of nuclear data evaluation, comprising the following steps: S1, selecting nuclides to be evaluated in a nuclear system to be analyzed; S2, selecting the nuclear cross section to be evaluated for each nuclide; S3, respectively calculating the sensitivity of each nuclear cross section selected in step S2; S4, selecting covariance data corresponding to each nuclear cross section and adjusting or estimating the covariance data; S5, respectively calculating the uncertainty Unc of each covariance matrix for keff k ; S6. Calculate the uncertainty Unc of keff caused by the nuclear cross section deviation of the nuclear system. The method provided by the present invention calculates the influence of each covariance matrix on the uncertainty of keff through the nuclear cross section sensitivity data and covariance data, and can quantitatively obtain the uncertainty value of keff caused by its nuclear cross section deviation, guiding the design and analysis and evaluation work.

Description

Technical Field

[0001] The invention belongs to the technical field of nuclear data evaluation, and in particular relates to a method for evaluating keff uncertainty caused by a nuclear cross section. Background Art

[0002] When evaluating the critical safety characteristics of a nuclear system, it is necessary to evaluate the uncertainty caused by various factors of the nuclear system, among which the uncertainty caused by the nuclear cross section is a very important aspect. Since the nuclear cross section will produce certain deviations during the measurement process, and according to its measurement principles and methods, the deviations will have certain correlations between different energy groups, different cross sections and even different nuclides, this correlation will cause an overall deviation in the nuclear cross section evaluation results, and will also cause an overall deviation in the keff (effective multiplication factor) calculation results based on this nuclear cross section data. Therefore, it is necessary to evaluate the impact of this correlation. This correlation is generally reflected in the covariance data. Due to the advancement of nuclear data evaluation technology in recent years, a considerable amount of covariance data information has been recorded in the nuclear data, which makes it possible to evaluate the keff uncertainty caused by nuclear cross section deviations.

[0003] At the same time, as the calculation program becomes more mature, various methods of calculating nuclear cross-section sensitivity using the Monte Carlo method can be implemented in the program. At the same time, with the development of computer technology, large-scale and precise calculation of nuclear cross-section sensitivity of nuclear systems is becoming more and more convenient. Summary of the invention

[0004] In order to solve the defects of the prior art, the purpose of the present invention is to provide a method for evaluating the keff uncertainty caused by nuclear section deviation, which can simultaneously give the influence of each section and the correlation between sections on the keff uncertainty of the nuclear system, and guide the design and nuclear data analysis and evaluation work.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0006] A method for evaluating the keff uncertainty caused by nuclear cross-section deviation comprises the following steps:

[0007] S1. Select the nuclides to be evaluated in the nuclear system to be analyzed;

[0008] S2. Select the nuclear cross section that needs to be evaluated for each nuclide;

[0009] S3, respectively calculating the sensitivity of each nuclear cross section selected in step S2;

[0010] S4, selecting covariance data corresponding to each nuclear cross section and adjusting or estimating the covariance data;

[0011] S5. Calculate the uncertainty Unc of each covariance data for keffk ;

[0012] S6. Calculate the uncertainty Unc of keff caused by the nuclear cross section deviation of the nuclear system.

[0013] Further, in the method for evaluating keff uncertainty caused by nuclear cross-section deviation as described above, the nuclides selected in step S1 include nuclear materials, structural materials or moderator materials in the nuclear system.

[0014] Furthermore, in the above-mentioned method for evaluating the keff uncertainty caused by nuclear cross-section deviation, multiple types of nuclides are selected in step S1.

[0015] Further, in the method for evaluating the keff uncertainty caused by nuclear section deviation as described above, the nuclear section types selected in step S2 include elastic, (n, n'), (n, 2n), fission, (n, gamma), (n, p), (n, d), (n, t), (n, he-3), nubar and chi.

[0016] Furthermore, in the method for evaluating the keff uncertainty caused by nuclear cross-section deviation as described above, the nuclear cross-section type of each nuclide selected in step S2 is unique, that is, the same type of total cross section and component cross section cannot be selected at the same time.

[0017] Further, in the above-mentioned method for evaluating the keff uncertainty caused by the nuclear cross-section deviation, the calculation formula of the sensitivity in step S3 is:

[0018]

[0019] Among them, α represents the input parameter, k represents the output parameter, S k,α Indicates sensitivity.

[0020] Further, in the method for evaluating the keff uncertainty caused by nuclear cross-section deviation as described above, the covariance data in step S4 is a relative covariance matrix.

[0021] Further, in the above-mentioned method for evaluating the keff uncertainty caused by the nuclear cross-section deviation, the specific method for adjusting or estimating the covariance data in step S4 is:

[0022] The data whose diagonal elements in the covariance matrix are 0 or greater than a set threshold are adjusted to predetermined values, and the corresponding non-diagonal elements between unreasonable values ​​are adjusted to predetermined correlation values;

[0023] The covariance matrix corresponding to the cross section that does not exist in the nuclear database and must be considered for calculation is estimated and constructed in a manner of setting the diagonal elements to the predetermined values ​​and setting the non-diagonal elements to the predetermined associated values.

[0024] Further, in the above-mentioned method for evaluating the uncertainty of keff caused by nuclear cross-section deviation, the uncertainty calculation method of keff for each covariance data in step S5 is:

[0025]

[0026] Among them, C i,j,k represents the covariance matrix, i and j represent two cross sections corresponding to the covariance matrix, k represents the order of the covariance matrix, and m represents the total number of covariance matrices selected in step S4.

[0027] Further, in the method for evaluating the uncertainty of keff caused by the nuclear cross-section deviation as described above, the calculation method of the uncertainty of keff caused by the nuclear cross-section deviation of the nuclear system in step S6 is:

[0028]

[0029] The method for evaluating the keff uncertainty caused by nuclear cross-section deviation of the present invention has the following significant technical effects:

[0030] The present invention calculates the influence of each covariance matrix on the uncertainty of keff through nuclear cross-section sensitivity data and covariance data, and can quantitatively obtain the uncertain value of keff caused by its nuclear cross-section deviation, guide nuclear data evaluation workers to judge certain nuclides with greater influence and consider material replacement, etc., and at the same time, can guide nuclear data evaluation workers to pay attention to certain cross-sections with greater influence and guide evaluation and analysis work. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a flow chart of a method for evaluating keff uncertainty caused by nuclear cross-section deviation provided in a specific embodiment of the present invention;

[0032] Figure 2 It is another flow chart of the method for evaluating keff uncertainty caused by nuclear cross-section deviation provided by the present invention. DETAILED DESCRIPTION

[0033] The present invention is further described below in conjunction with specific embodiments and the accompanying drawings.

[0034] Figure 1 A flow chart of a method for evaluating keff uncertainty caused by nuclear cross-section deviation provided in a specific embodiment of the present invention is shown, and the method comprises the following steps:

[0035] S1. Select the nuclides to be evaluated in the nuclear system to be analyzed

[0036] Generally, it should include nuclear materials (such as U, Pu, etc.), main structural materials (such as Fe, Cr, Ni, etc.), main moderator materials (such as H, C, etc.), and other main materials. When it is impossible to determine which nuclides are more important, all nuclides can be selected as analysis objects.

[0037] S2. Select the nuclear cross section that needs to be evaluated for each nuclide

[0038] This nuclear cross section should be unique. If the total inelastic scattering cross section is selected, each component cross section of the inelastic scattering cross section should not be selected. The selected cross sections should generally include elastic, (n, n'), (n, 2n), fission, (n, gamma), (n, p), (n, d), (n, t), (n, he-3), nubar and chi cross sections. Of course, different nuclides do not have all these cross sections, and they should be excluded in the calculation (for example, H does not have a fission cross section). At the same time, this step should specify the cross sections that must be considered for calculation.

[0039] S3, calculate the sensitivity of each nuclear cross section selected in step S2

[0040] Sensitivity is defined as the effect of a percentage change in a certain response caused by a certain percentage change in the input parameter. The calculation method is shown in formula (1).

[0041]

[0042] Among them, α represents the input parameter, k represents the output parameter, S k,α Represents sensitivity.

[0043] There are generally direct perturbation method, differential operator method and adjoint calculation method for calculating sensitivity. These methods have their own advantages and disadvantages. Different methods should be selected according to different calculation objects and calculation environments. Since the calculation of sensitivity is not the focus of this invention, it will not be described in detail here. The calculated sensitivity data energy group structure should correspond to the covariance data energy group structure.

[0044] S4. Select the corresponding covariance data and adjust or estimate the covariance data

[0045] The covariance data referred to here should be the relative covariance matrix. Since some unreasonable values ​​will appear in the covariance data during the evaluation and production process, such as deviations that are too large or too small, these unreasonable values ​​should be adjusted. At the same time, in order to meet the characteristics of the covariance matrix, the relevant data should also be adjusted. Generally, the diagonal elements in the covariance matrix (symmetric matrix) are replaced with values ​​that are 0 or greater than a certain value (such as 10) (such as d = 0.04), and at the same time, the corresponding non-diagonal elements between unreasonable values ​​are replaced with a certain associated value (such as d' = d / 2 = 0.02).

[0046] At the same time, the covariance matrix in the nuclear database is not complete, and the covariance matrix corresponding to the cross section that must be considered for calculation should be estimated and constructed. The matrix is ​​constructed in such a way that the diagonal elements are d (such as 0.04) and the non-diagonal elements can be d / 2 (such as 0.02).

[0047] S5. Calculate the uncertainty Unc of each covariance data for keff k

[0048] This calculation includes all the covariance data selected in step S4, and the covariance data is denoted as C i,j,k .

[0049] The influence of different covariance matrices on keff k See formula (2).

[0050]

[0051] Among them, i and j represent two cross sections corresponding to the covariance matrix, k represents the order of the covariance matrix, and m represents the number of covariances selected in step S4.

[0052] S6. Calculate the keff uncertainty Unc caused by the nuclear cross section deviation of the nuclear system

[0053] Based on the result of step S5, the keff uncertainty caused by all nuclear cross-section deviations and correlations of the nuclear system is calculated. The calculation method is shown in formula (3).

[0054]

[0055] In order to more clearly describe the technical solution of the present invention, two group structures are taken as an example for description.

[0056] Step 1: Select two nuclides of a nuclear system to be analyzed and denote them as N 1 , N 2 .

[0057] Step 2: Select two cross sections of each nuclide, a total of four cross sections, denoted as R 11 , R 12 , R 21 , R 22 . These four sections are the sections that must be considered in the calculation.

[0058] Step 3: Use a computer program to calculate the sensitivity of the four cross sections in step 2 to keff. The sensitivity of the four cross sections in the two groups of structures to keff are:

[0059]

[0060] Step 4: Select the covariance data in the kernel database that is related to step 2

[0061]

[0062] It can be seen that there are R 11 , R 12 and R 21 The covariance between the three cross-sectional self-energy groups, and R 11 With R 12 The covariance between the two sections. The R 22 The cross-sectional covariance is not available in the database and needs to be estimated. The covariance matrix is ​​constructed using diagonal elements of 0.04 and non-diagonal elements of 0.02. 11 With R 12 The covariance data between the two sections has unreasonable values, among which the diagonal elements 15 and 20 are too large, so they are replaced with 0.04, and the corresponding non-diagonal elements are replaced with 0.02. The covariance data used in the final calculation is:

[0063]

[0064] Step 5: Calculate the uncertainty of different covariance matrices on keff. Using the results in steps 3 and 4, we can get the influence of different covariance matrices on keff as follows:

[0065]

[0066] Step 6: Calculate the keff uncertainty caused by all nuclear cross section deviations in the nuclear system

[0067] According to the results of step 5, the keff uncertainty caused by all nuclear cross-section deviations and correlations of the nuclear system is obtained as follows:

[0068] Unc=0.2961

[0069] The present invention calculates the influence of each covariance matrix on the uncertainty of keff through nuclear cross-section sensitivity data and covariance data, and can quantitatively obtain the uncertain value of keff caused by its nuclear cross-section deviation, guide nuclear data evaluation workers to judge certain nuclides with greater influence and consider material replacement, etc., and at the same time, can guide nuclear data evaluation workers to pay attention to certain cross-sections with greater influence and guide evaluation and analysis work.

[0070] The above embodiments are merely illustrative of the present invention, and the present invention may also be implemented in other specific ways or other specific forms without departing from the gist or essential features of the present invention. Therefore, the described embodiments should be considered illustrative rather than restrictive in any respect. The scope of the present invention should be described by the appended claims, and any changes equivalent to the intent and scope of the claims should also be included within the scope of the present invention.

Claims

1. A method for evaluating the uncertainty of keff caused by nuclear cross-section deviation, comprising the following steps: S1. Select the nuclides to be evaluated in the nuclear system to be analyzed; S2. Select the nuclear cross section that needs to be evaluated for each nuclide; S3, respectively calculating the sensitivity of each nuclear cross section selected in step S2, the calculation formula of the sensitivity is: Among them, α represents the input parameter, k represents the output parameter, S k,α Indicates sensitivity; S4, selecting covariance data corresponding to each nuclear cross section and adjusting or estimating the covariance data; S5. Calculate the uncertainty Unc of each covariance data for keff k , the calculation method is: Among them, C i,j,k represents the covariance matrix, i and j represent two cross sections corresponding to the covariance matrix, k represents the order of the covariance matrix, and m represents the total number of covariance matrices selected in step S4; S6. Calculate the uncertainty Unc of keff caused by the nuclear cross section deviation of the nuclear system. The calculation method is:

2. The method for evaluating keff uncertainty caused by nuclear cross-section deviation according to claim 1, characterized in that: The nuclides selected in step S1 include nuclear materials, structural materials or moderator materials in the nuclear system.

3. The method for evaluating keff uncertainty caused by nuclear cross-section deviation according to claim 2, characterized in that: The nuclear cross-section types selected in step S2 include elastic, (n, n'), (n, 2n), fission, (n, gamma), (n, p), (n, d), (n, t), (n, he-3), nubar, and chi.

4. The method for evaluating keff uncertainty caused by nuclear cross-section deviation according to claim 3, characterized in that: The nuclear cross section type of each nuclide selected in step S2 is unique, that is, the same type of total cross section and component cross section cannot be selected at the same time.

5. The method for evaluating keff uncertainty caused by nuclear cross-section deviation according to claim 1, characterized in that: The covariance data in step S4 is a relative covariance matrix.

6. The method for evaluating keff uncertainty caused by nuclear cross-section deviation according to claim 5, characterized in that: The specific method for adjusting or estimating the covariance data in step S4 is: The data whose diagonal elements in the covariance matrix are 0 or greater than a set threshold are adjusted to predetermined values, and the corresponding non-diagonal elements between unreasonable values ​​are adjusted to predetermined correlation values; The covariance matrix corresponding to the cross section that does not exist in the nuclear database and must be considered for calculation is estimated and constructed in a manner of setting the diagonal elements to the predetermined values ​​and setting the non-diagonal elements to the predetermined associated values.

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