Method, system and equipment for adjusting resonance integral in physical multi-group constant library of reactor core

Abstract

The invention relates to a method, a system and equipment for adjusting resonance integral in a physical multi-group constant library of a reactor core, and the method comprises the following steps: (S1) determining a descent gradient of a steepest descent method for optimizing the resonance integral for a selected sample experiment group; (S2) determining an optimized and adjusted resonance integral according to a gradient descent direction of a steepest descent method, and merging the resonance integral into a main library of target nuclides; (S3) making subgroup parameters based on the optimized and adjusted resonance integral; (S4) generating an optimized and adjusted reactor core physical multi-group constant library; and (S5) carrying out benchmark inspection on the optimized reactor core physical multi-group constant library. According to the method, the accuracy of effective multiplication factors and other integral quantities obtained through calculation of the reactor core physical multi-group constant library based on the subgroup method during reactor physical calculation can be ensured, and meanwhile, the universality of the reactor core physical multi-group constant library is also expanded.

Description

Technical Field

[0001] The invention belongs to a data processing method of a nuclear database, and in particular relates to a resonance integral adjustment method, system and equipment within a core physics multi-group constant library. Background Art

[0002] Reactor neutron physics calculation is the most basic research content in nuclear reactor system design and safety analysis. The accuracy and confidence of its calculation results will directly affect the safety and economic evaluation of nuclear reactors. The core physics multi-group constant library provides cross-section data and burnup data for nuclear reactor neutron physics calculations. It is the basis and guarantee of reactor physics calculations. The accuracy of the multi-group constant data in the library directly affects the accuracy of reactor physics calculations and reactor design. The resonance phenomenon refers to the phenomenon that incident particles with certain specific energies combine with atomic nuclei to form metastable composite nuclei. When the energy of the incident neutron approaches these energy points, the reaction cross section will increase sharply. The cross section of some heavy nuclei in reactor fuels changes dramatically with energy in some energy ranges. In some energy ranges, the cross section shows a sharp resonance peak. The reaction cross section at the resonance peak shows an exponential change, which leads to a valley in the energy spectrum at the resonance peak due to the energy self-screening effect, and the neutron flux density value is very low. Because of the complex resonance self-screening phenomenon, the resonance data has a great influence on the accuracy of transport calculations in reactor physics calculations. Accurate calculation of effective resonance cross section is the premise of reactor core neutron physics calculation. The deterministic calculation methods for resonance self-screening effect mainly include ultrafine group method. [1-2] , Equivalence Theory Method [3-5] and subgroup methods [6-7] . The ultrafine group method accurately describes the cross-sectional changes of the resonance group detention fluctuations in a manner close to continuous energy. Its advantage is high accuracy, but its disadvantage is low computational efficiency. The equivalent theory method is to establish an equivalent relationship between uniform problems and non-uniform problems by calculating the probability of the first neutron collision, and then obtain the background cross section of the actual problem through approximate calculations, and then obtain the effective resonance cross section through the background cross section interpolation resonance integral table. This method is closely related to the geometry and materials of the actual problem. For increasingly complex new reactors, this method cannot guarantee accuracy. The subgroup method is different from the traditional method. It discretizes the resonance group from the perspective of the cross section. Nikolaev of the Soviet Union [6] The first person to propose the concept of subgroups was Levitt of the United States. [7]In order to solve the problem of cross-section calculation in the indistinguishable resonance zone, a resonance calculation method based on probability table is proposed to express the violently fluctuating resonance peak in the form of probability density, and solve the effective resonance cross section through the cross-section distribution probability. The subgroup method extends the idea of ​​probability table to the entire resonance energy segment, and describes the numerical change of the cross section and its corresponding probability density through subgroup cross sections and subgroup weights. This method improves the calculation accuracy while improving the calculation efficiency, so the subgroup method has become a hot spot for advanced reactor resonance calculations. The resonance integral is the data base point for the calculation of subgroup parameters. The conventional subgroup parameters are calculated based on the resonance integral under uniform conditions, which will lead to 238 To solve this problem, Hur ia [9] Based on the actual PWR calculation experience, 238 The value of the U resonance integral data is reduced by about 3.4%, thereby improving the calculation accuracy of the resonance cross section. Stamm'ler [8] The idea of ​​using non-uniform resonance integrals instead of uniform resonance integrals is to obtain the corresponding relationship between the problem-related background cross section and the resonance integral by solving the ultrafine group slowing-down equation under non-uniform conditions.

[10] He Liu [11-12] et al. applied the non-uniform resonance integral table to the embedded resonance self-screening calculation method.

[13] This method is also used in the calculation of subgroup parameters, which can improve the calculation accuracy of specific problems. However, the preparation process of inhomogeneous resonance integrals is complicated and lacks universality. At the same time, referring to the nuclear data adjustment method, there are two main types of nuclear data adjustment methods: deterministic adjustment method based on the sensitivity coefficient of integral parameters to nuclear data [14-16] and adjustment methods based on random sampling methods [17-20] . Deterministic methods mainly include the generalized least squares method based on Bayesian inference theory and the extended nuclear data adjustment method and extended deviation factor method based on Bayesian inference theory. The latter two methods derive the nuclear data adjustment formula by minimizing the variance of the calculated integral parameters of the designed nuclear reactor. The nuclear data adjustment methods based on random sampling mainly include the Monte Carlo Bayesian analysis method and the Bayesian Monte Carlo method, the forward-backward Monte Carlo method and the full Monte Carlo method. Therefore, an optimization algorithm is used to optimize the resonance data, that is, the resonance integral in the library, to improve the accuracy of the core physics multi-group constant library based on the subgroup method, which can not only ensure accuracy but also expand versatility.

[0003] The above cited documents are as follows:

[0004] [1]Sugimura N, Yamamoto A. Resonance Treatment Based on Ul tra-Fine-Group Spectrum Calculation in the AEGIS Code[J]. Journal of Nuclear Science and Technology, 2007, 44(7):958-966.

[0005] [2]Ishiguro Y,Takano H.PEACO:A Code for Calculation of GroupConstant of Resonance Energy Region in Heterogeneous Systems[R].Japan:JapanAtomic Energy Research Institute,1971.

[0006] [3]Askew J, Fayers F, Kemshel l P.General Description of The Latt iceCode WIMS[J].Journal of the British Nuclear Energy Society,1966,5(4):564-585

[0007] [4] Zhang Qian. Research on advanced resonance self-screening calculation method based on equivalent theory[D]. Xi'an: Xi'an Jiaotong University, 2016

[0008] [5]Yuxuan Liu.A Full Core Resonance Self-Shielding Method Accounting for Temperature-Dependent Fuel Subregions and Resonance Interference[D].Ann Arbor:University of Michigan,2015

[0009] [6]Nikolaev M,Ignatcv A,Isaev N,et al.The Method of Subgroups forCons idering the Resonance Structure of Cross Sect ions in NeutronCalculations[J].Atomnaya Energiya,1970,30:528-533

[0010] [7]Levi tt L.The Probabi l ity Table Method for Treating UnresolvedNeutron Resonances in Monte Carlo Calculat ions[J].Nuclear Science andEngineering,1972,49(4):450-457

[0011] [8]Stamm’ler R.HELIOS Methods[R].Sweden:StudsvikScandpower,2008.

[0012] [9]Huria H,Ouis loumen M.ENDF / B-VI:238U Resonance Integral Reduction-A Closer Look[C].Transact ions of the Amer ican Nuclear Society.USA,1997,76:329-330.

[0013]

[10] Hong S G,Kim K S.Iterat ive Resonance Self-Shielding Methods Using Resonance Integral Table in Heterogeneous Transport Latt ice Calculations[J].Annals of Nuclear Energy,2011,38(1):32-43

[0014]

[11] Liu Y,Martin W,Wi l l iams M,et al.A Ful l-Core Resonance Self-Shielding Method Us ing a Cont inuous-Energy Quas i-One-Dimens ional Slowing-Down Solut ion that Accounts for Temperature-Dependent Fuel Subregions andResonance Interference[J].Nuclear Science and Engineering,2015,180(3):247-272.

[0015]

[12] Liu Y,Mart in W.Assessment of Homogeneous and HeterogeneousResonance Integral Tables and Their Appl icat ions to the Embedded Self-Shielding Method[J].Annals of Nuclear Energy,2016,92:186-197

[0016]

[13] Joo H G,Kim G Y,Pogosbekyan L.Subgroup Weight Generat ion Basedon Shielded Pin-cel l Cross Section Conservat ion[J].Annals of NuclearEnergy,2009,36(7):859-868.

[0017] ALDAMA DL,LESZCZYNSKI F,TRKOV A.WIMS-D Library Update,Final report ofa coordinated research project[R].Internat ional Atomic Energy Agency,2003.

[0018]

[14] Yokoyama K,Ki tada T.General ized formulat ion of extended cross-sect ion adjustment method based on minimum variance unbiased l inear es timation[J].Journal of Nuclear Science and Technology.2019,56(1):87-104.

[0019]

[15] Yokoyama K,Yamamoto A,Ki tada T.Dimens ion-reduced cross-sect ionadjustment method based on minimum variance unbiased est imat ion[J].Journalof Nuclear Science and Technology.2018,55(3):319-334.

[0020]

[16] Pel loni S,Rochman D.Enhancements along with appl ication of theAsymptotic Progress ing nuclear data Incremental Adjustment(APIA)methodologyby individual ass imi lations of fast reactor data[J].Annals of NuclearEnergy.2019,129:79-89.

[0021]

[17] Siefman,Daniel et al.“Stochast ic vs.sens i tivity-basedintegral parameter and nuclear data adjustments.”The European Phys icalJournal Plus 133(2018):1-10.

[0022]

[18] Takeda S,Ki tada T.Individual Adjustment of Independent Cross-Section Set Based on Bayes ian Theory[J].Nuclear Science andEngineering.2021,195(5):496-508.

[0023]

[19] Yokoyama K,Ishikawa M.Use and Impact of Covariance Data in theJapanese Latest Adjusted Library ADJ2010 Based on JENDL-4.0[J].Nuclear DataSheets.2015,123:97-103.

[0024]

[20] Palmiott i G, Salvatores M. Revisiting the bias factormethodologies for the validation of fas t tes t reactors[J].Annals ofNuclear Energy.2020,145:107591. Summary of the invention

[0025] The purpose of the present invention is to address the deficiencies in the prior art and to provide a method, system and device for adjusting the resonance integral in a core physics multi-group constant library based on a subgroup method, which can ensure the accuracy of integral quantities such as the effective multiplication factor calculated by the core physics multi-group constant library based on the subgroup method during reactor physics calculations, while also expanding the versatility of the core physics multi-group constant library.

[0026] To achieve the above object, the technical solution of the present invention is as follows:

[0027] A method for adjusting the resonance integral in a core physics multi-group constant library comprises the following steps:

[0028] (S1) determining a descent gradient of a steepest descent method for optimizing a resonance integral for a selected sample experimental group;

[0029] (S2) determining the optimized and adjusted resonance integral according to the gradient descent direction of the steepest descent method, and merging it into the main library of the target nuclide;

[0030] (S3) generating subgroup parameters based on the optimized and adjusted resonance integral;

[0031] (S4) generating an optimized and adjusted core physics multi-group constant library;

[0032] (S5) Benchmarking the optimized core physics multi-group constant library.

[0033] Further, in a specific embodiment, in the above-mentioned method for adjusting the resonance integral of the core physics multi-group constant library, the method for determining the descent gradient in step (S1) is as follows:

[0034] First, based on the initial resonance integral RI 0 For the selected sample experimental group, the component calculation program is used to perform transport calculations to obtain the corresponding integral amount, and then the initial total chi-square value χ is calculated by the integral amount. 0 2 , the calculation formula is as follows:

[0035]

[0036] Among them, k m is the integral calculated from the mth sample experiment, i.e., the effective multiplication factor; EXP m is the experimental value obtained by measuring the mth sample experiment;

[0037] Then, by perturbing the resonance integral, the i-th generation resonance integral RI is obtained from formula (2): i ,

[0038] RI i =RI i-1 (1-c i )(2)

[0039] Among them, RI i is the resonance integral under each background cross section of the i-th generation; RI i-1 is the resonance integral under each background cross section of the i-1th generation; c i is the i-th generation resonance integrated perturbation coefficient;

[0040] Based on the i-th generation resonance integral RI i For the selected benchmark sample experimental group, the component calculation program is used to perform transport calculations to obtain the corresponding integral (i.e., effective multiplication factor), and then the total chi-square value χ is calculated by the integral. i 2 ;

[0041] The descent gradient of the steepest descent method is shown in formula (3):

[0042]

[0043] Among them, χ i 2is the total chi-square value obtained by the integral calculated by the i-th generation resonance integral; i-1 2 is the total chi-square value obtained by calculating the integral of the i-1th generation resonance integral; c i is the i-th generation resonance integrated perturbation coefficient.

[0044] Further, in a specific embodiment, in the above-mentioned method for adjusting the resonance integral of the core physics multi-group constant library, the objective function of the steepest descent method gradient descent in step (S2) is shown in formula (4):

[0045]

[0046] Among them, c i is the i-th generation resonance integral perturbation coefficient; α is the descending step size; is the descending direction; c i+1 is the i+1th generation resonance integrated perturbation coefficient;

[0047] Then, the optimized and adjusted resonance integral can be obtained through formula (2).

[0048] Further, in a specific embodiment, in the method for adjusting the resonance integral in the core physics multi-group constant library as described above, in step (S3), a subgroup parameter fitting program is used to obtain the optimized subgroup parameters based on the optimized adjusted resonance integral through a fitting method.

[0049] Furthermore, the subgroup parameters include two parts: subgroup cross section and subgroup probability.

[0050] Further, in a specific embodiment, in the above-mentioned method for adjusting the resonance integral in the core physics multi-group constant library, in step (S4), the optimized subgroup parameters are added to the main library file, and the main library of the target nuclide with the subgroup parameters is combined with the main library of other nuclides to generate the optimized core physics multi-group constant library T i+1 , then based on the optimized core physics multi-group constant library T i+1 And the sample experimental group performs reactor physics calculations to obtain the i+1 generation integral. Through optimization iteration, when the total chi-square value of the i+1 generation χ i+1 2 and the total chi-square value x of the i-th generation i 2 The difference is less than the convergence criterion 1E-5, then the resonance integral that meets the standard and the corresponding core physics multi-group constant library T are obtained. final .

[0051] Further, in a specific embodiment, in the resonance integral adjustment method for the core physics multi-group constant library as described above, in step (S5), the benchmark test includes a critical benchmark test and a burnup benchmark test; the critical benchmark test is to select fast spectrum, intermediate energy spectrum, and thermal spectrum benchmark experiments from the International Nuclear Criticality Safety Manual ICSBEP2006 and the Cross-Section Evaluation Working Group Benchmark Experiment Manual ENDF-202 to test the core physics multi-group constant library; the burnup benchmark test is to select a burnup benchmark experiment from the spent fuel isotopic composition database SFCOMPO-2 (Spent Fuel Isotopic Composition Database), use component programs to perform modeling and calculations, compare the calculation results with the experimental results, and evaluate the accuracy of the burnup calculation.

[0052] Furthermore, the benchmark inspection of the core physics multi-group constant library mainly inspects the key nuclides commonly used in nuclear devices.

[0053] A core physics multi-group constant library resonance integral adjustment system, comprising:

[0054] A steepest descent gradient calculation module, used for determining the descent gradient of the steepest descent method for optimizing the resonance integral for the selected sample experimental group;

[0055] A resonance integral optimization and adjustment module is used to determine the optimized and adjusted resonance integral according to the gradient descent direction of the steepest descent method, and merge it into the main library of the target nuclide;

[0056] A subgroup parameter making module, based on the optimized and adjusted resonance integral, uses a subgroup parameter fitting program to make subgroup parameters;

[0057] The core physics multi-group constant library production module generates an optimized and adjusted core physics multi-group constant library based on the optimized sub-group parameters;

[0058] The core physics multi-group constant library benchmark verification module is used to perform benchmark verification on the optimized core physics multi-group constant library.

[0059] The present invention further provides a device, including a storage medium and a processor, wherein the storage medium stores a computer program, and when the processor executes the computer program, the resonance integral adjustment method within the core physics multi-group constant library as described above is implemented.

[0060] The beneficial effects of the present invention are as follows: The present invention uses the steepest descent method to adjust the resonance integral table in the core physics multi-group constant library by an iterative optimization method, establishes an automated process for optimizing resonance integrals, and provides a new solution to the problem of insufficient accuracy in critical calculations at the beginning of the life of the core physics library. The method can ensure the accuracy of integral quantities such as the effective multiplication factor calculated by the core physics multi-group constant library based on the subgroup method during reactor physics calculations, and also expand the versatility of the core physics multi-group constant library. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a schematic diagram of a resonance integral adjustment method in a core physics multi-group constant library based on a subgroup method of the present invention;

[0062] Figure 2 Schematic diagram of the process of the multi-group constant library production system TPAMS in an embodiment of the present invention

[0063] Figure 3 A schematic diagram of a flow chart of adjusting the resonance integral by an optimization iterative algorithm in an embodiment of the present invention;

[0064] Figure 4 A schematic diagram of a geometric model established for the HEU-SOL-THERM-027 benchmark problem in an embodiment of the present invention;

[0065] Figure 5 Schematic diagram of the calculation model of SF95 series samples in an embodiment of the present invention. DETAILED DESCRIPTION

[0066] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0067] The resonance integral is the data base point for subgroup parameter calculation. The core physics multi-group constant library based on the subgroup method contains three types of resonance-related data. The first type is the resonance integral table data of the traditional absorption cross section and generation cross section. The second type is the subgroup parameter data used by the subgroup resonance method. The third type is the resonance integral data of the scattering cross section and the lower scattering cross section. Referring to the deterministic method in the nuclear data adjustment method, the technical solution for optimizing and adjusting the resonance integral in the core physics multi-group constant library includes two parts: one is to use the optimal iterative algorithm to adjust the resonance integral in the core physics multi-group constant library, and then produce the optimized subgroup parameters; the second is to perform a benchmark test on the adjusted core physics multi-group constant library. The adjustment process is as follows: Figure 1 shown.

[0068] (I) Optimal iterative algorithm to adjust the resonance integral in the core physics multi-group constant library

[0069] The steepest descent method is one of the most commonly used methods in optimization algorithms. The steepest descent method is an iterative algorithm for solving unconstrained optimization problems. Its core principle is to find the minimum value of the function along the direction where the objective function descends fastest (that is, the negative gradient direction of the point) at each iteration point. Specifically, through the Taylor expansion, it can be analyzed that the speed of function descent is mainly determined by the terms related to the gradient, and then the direction of the steepest descent is determined. The iterative process starts from an initial point and updates the position of the point according to a certain iterative formula by adding the product of the step size and the search direction (negative gradient direction). The step size can be determined by precise or imprecise line search.

[0070] 1. Steepest descent gradient calculation

[0071] First, determine the benchmark sample experimental group based on your own needs. Based on the initial resonance integral RI 0 For the benchmark sample experimental group, component calculation programs such as HELIOS and CASMO were used to perform transport calculations and obtain the corresponding integral quantities (effective multiplication factor k eff ). Calculate the initial total chi-square value x by integrating the quantity 0 2 The calculation formula is as follows:

[0072]

[0073] Among them, k m is the integral calculated from the mth sample experiment, i.e., the effective multiplication factor; EXP m is the experimental value obtained by measuring the mth sample experiment.

[0074] Then, by perturbing the resonance integral, the first generation resonance integral RI is obtained according to formula (2): 1 , based on the first generation resonance integral RI 1 For the benchmark sample experimental group, the component calculation program was used to perform transport calculations and the corresponding integral quantities (effective multiplication factor k eff ), calculate the total chi-square value x by integrating 1 2 .

[0075] RI i =RI i-1 (1-c i )(2)

[0076] Among them, RI i is the resonance integral under each background cross section of the i-th generation; RI i-1 is the resonance integral under each background cross section of the i-1th generation; c i is the resonance integrated perturbation coefficient.

[0077] By analogy, we can get the i-th generation resonance integral RI i , based on the i-th generation resonance integral RI i For the selected benchmark sample experimental group, the component calculation program is used to perform transport calculations to obtain the corresponding integral (i.e., effective multiplication factor), and then the total chi-square value χ is calculated by the integral. i 2 .

[0078] Then, the descent gradient of the steepest descent method is as shown in formula (3):

[0079]

[0080] Among them, χ i 2 is the total chi-square value obtained by the integral calculated by the i-th generation resonance integral; i-1 2 is the total chi-square value obtained by calculating the integral of the i-1th generation resonance integral; c i is the i-th generation resonance integrated perturbation coefficient.

[0081] 2. Optimization algorithm to obtain adjusted resonance integral

[0082] The chi-square value calculated from the sample experimental group is used to find the direction of gradient descent, and the resonance integral with the optimal chi-square value is found based on the gradient descent direction, which is then merged into the main library of the target nuclide for subsequent subgroup parameter fitting and core physics multi-group constant library production. The system produces a core physics multi-group constant library based on the subgroup method.

[0083] The objective function of the steepest descent method gradient descent is shown in formula (4):

[0084]

[0085] Among them, c i is the i-th generation resonance integral perturbation coefficient; α is the descending step size; is the descending direction; c i+1 is the i+1th generation resonance integrated perturbation coefficient.

[0086] Then, the optimized and adjusted resonance integral can be obtained through formula (2).

[0087] 3. Create subgroup parameters based on optimized resonance integrals

[0088] Subgroup parameters are important parameters required for reactor physical resonance calculations. There are two main methods for generating subgroup parameters, namely fitting method and moment method. This section mainly uses the fitting method to produce subgroup parameters. Based on the optimization solution method, all background section points and corresponding resonance integrals in the resonance table are used for fitting, which can cover a wide enough range to avoid extrapolation. At the same time, given appropriate constraints, the required subgroup parameters can be obtained. Based on the existing subgroup parameter fitting KYROS program, the optimized subgroup parameters are obtained based on the adjusted resonance integral.

[0089] 4. Create a multi-group constant library for core physics

[0090] The optimized subgroup parameters are added to the main library file, and the main library of the target nuclide with subgroup parameters and other nuclide main libraries are combined to generate the optimized core physics multigroup constant library T through the core physics multigroup constant library production system. i+1 . At the same time, the optimized core physics multi-group constant library T i+1 And the sample experimental group performs reactor physics calculations to obtain the i+1 generation integral k eff,i+1 , through optimization iteration until the resonance integral that meets the standard and the corresponding core physics multi-group constant library T are found final .

[0091] (II) Benchmarking of the adjusted core physics multi-group constant library

[0092] Theoretically, the macro benchmark test of the group constant library should cover all materials and the entire energy range in the library, but this is impossible in reality. Limited benchmark experiments have limited coverage of nuclides and energy spectra, usually only covering major fission nuclides, structural materials, light nuclides, fission products, etc. The coverage of the energy range is restricted by the sensitivity range of the experimental device to a certain nuclear reaction. Therefore, the benchmark test of the group constant library mainly tests the key nuclides commonly used in nuclear devices, and the selection of experimental devices is also selected according to the application type in order to test the accuracy of the database. The macro test of the core physics multi-group constant library selects two types of experiments: criticality benchmark experiments and burnup benchmark experiments. The criticality benchmark test selects fast spectrum, intermediate energy spectrum, and thermal spectrum benchmark experiments from the International Nuclear Criticality Safety Manual ICSBEP2006 and the Cross-Section Evaluation Working Group Benchmark Experiment Manual ENDF-202 to test the core physics library. It is necessary to use component programs to model and calculate the selected benchmark questions and compare them with the experimental benchmark values. The burnup benchmark test is to select burnup benchmark experiments from the spent fuel isotopic composition database SFCOMPO-2 (Spent Fuel Isotopic Composition Database), use component programs to build models and calculate, compare the calculated results with the experimental results, and evaluate the accuracy of the burnup calculation.

[0093] At the same time, the present invention also provides a system and device for adjusting the resonance integral of a core physics multi-group constant library. The software system corresponding to the above-mentioned method for adjusting the resonance integral of a core physics multi-group constant library based on the subgroup method includes:

[0094] A steepest descent gradient calculation module, used for determining the descent gradient of the steepest descent method for optimizing the resonance integral for the selected sample experimental group;

[0095] A resonance integral optimization and adjustment module is used to determine the optimized and adjusted resonance integral according to the gradient descent direction of the steepest descent method, and merge it into the main library of the target nuclide;

[0096] A subgroup parameter making module, based on the optimized and adjusted resonance integral, uses a subgroup parameter fitting program to make subgroup parameters;

[0097] The core physics multi-group constant library production module generates an optimized and adjusted core physics multi-group constant library based on the optimized sub-group parameters;

[0098] The core physics multi-group constant library benchmark verification module is used to perform benchmark verification on the optimized core physics multi-group constant library.

[0099] A hardware device includes a storage medium and a processor, wherein the storage medium stores a computer program, and when the processor executes the computer program, the resonance integral adjustment method in a core physics multi-group constant library as described above is implemented.

[0100] Example

[0101] The method of the present invention is described in detail below in conjunction with the detailed information of the selected specific sample experimental group.

[0102] (I) Optimal iterative algorithm to adjust the resonance integral in the core physics multi-group constant library

[0103] (1) Steepest descent gradient calculation

[0104] First, determine the benchmark sample experimental group according to your own needs. Based on the initial resonance integral RI 0 And based on the initial resonance integral RI 0 The core physics multi-group constant library T 0 For the benchmark sample experimental group, the component calculation program was used to perform transport calculations and the corresponding integral quantities (effective multiplication factor k eff ) Calculate the initial total chi-square value χ by integrating the amount 0 2 The sample experimental groups are shown in Table 1:

[0105] Table 1 Detailed information of sample experimental groups

[0106]

[0107] The calculation principle is as described in formula (1) to formula (4) above. The optimization algorithm program is developed based on Python. The code (excerpt) is as follows:

[0108]

[0109]

[0110] (2) Optimization algorithm obtains adjusted resonance integral

[0111] The chi-square value calculated from the sample experimental group is used to find the direction of gradient descent, and the resonance integral with the optimal chi-square value is found based on the gradient descent direction, which is then merged into the main library of the target nuclide for subsequent subgroup parameter fitting and core physics multi-group constant library production. The system produces a core physics multi-group constant library based on the subgroup method.

[0112] (3) Generate subgroup parameters based on optimized resonance integral

[0113] The subgroup parameters include subgroup cross section and subgroup probability. The constrained least squares method is used to fit the subgroup parameters. Finally, the subgroup parameters of 7 subgroups and 4 subgroups are obtained through fitting calculations, and finally merged into the main library to form a .hel file for subsequent production of the core physics multi-group constant library.

[0114] (4) Preparation of the adjusted core physics multi-group constant library

[0115] The core physics multi-group constant library production system combines the main library of the target nuclide with subgroup parameters and the main library of other nuclides to generate an adjusted core physics multi-group constant library. Then, based on the adjusted core physics multi-group constant library, the component calculation program is used to perform transport calculations on the sample experimental group to obtain the second-generation integral quantity (effective multiplication factor k eff ), and re-optimize and iterate until a resonance integral that meets the criteria and the corresponding core physics multi-group constant library are found.

[0116] The multi-group constant library production system TPAMS developed by China Nuclear Data Center is Figure 2 shown.

[0117] The process of determining the optimal resonance integral through step-by-step optimization iteration is as follows Figure 3 As shown, first the initial resonance integral perturbation coefficient c 0 = 0, the first generation core physics multi-group constant adjustment library T is produced through the TPAMS system 0 , the 0th generation chi-square value χ is calculated according to the component calculation procedure 0 2 , and given the first generation resonance integral perturbation coefficient c 1= 0.05, and the first generation resonance integral RI is calculated according to formula (2) 1 , according to RI 1 The first generation of core physics multi-group constant adjustment library T was created by TPAMS system 1 , the total chi-square value of the first generation is calculated according to the component calculation procedure 1 2 According to the given initial value and formula (3), the descent gradient is calculated, and the next generation resonance integral perturbation coefficient c is obtained according to the descent gradient. The next generation resonance integral is calculated according to the resonance integral perturbation coefficient c, and then the next generation total chi-square value χ is obtained according to the component calculation program. 2 , and so on, when the total chi-square value of the i+1th generation is i+1 2 and the total chi-square value of the i-th generation i 2 If the difference is less than the convergence criterion 1E-5, it will jump out. i+1 Calculated RI i+1 This is the final adjusted resonance integral value.

[0118] (II) Benchmarking of the adjusted core physics multi-group constant library

[0119] There are two types of benchmark tests for the core physics multi-group constant library. The first is the criticality benchmark test, which verifies the basic data of each nuclide, such as the cross section, fission spectrum, and scattering cross section. Generally, fast spectrum, intermediate energy spectrum, and thermal spectrum benchmark experiments are selected from the International Nuclear Criticality Safety Manual ICSBEP2006, the Cross Section Evaluation Working Group Benchmark Experiment Manual ENDF-202, and the WIMS Update Plan (WLUP). The second is the burnup benchmark test, which verifies data such as fission yield and burnup chain. It is usually selected from the spent fuel isotope composition database SFCOMPO-2. Both of the above benchmark tests use component programs for modeling and calculation, and compare the calculation results with the experimental results to evaluate the accuracy of the core physics multi-group constant library.

[0120] (1) Critical benchmark inspection

[0121] This example uses the HEU-SOL-THERM-027 benchmark problem of high-enriched uranyl nitrate cylindrical barrels without reflection layers in ICSBEP as a representative to introduce the critical benchmark test. The experimental information of the HEU-SOL-THERM-027 benchmark problem is shown in Table 2, and the modeling geometry is as follows: Figure 4 As shown, the radius is 0.5 cm, the grid length is 1 cm, total reflection boundary conditions are defined around it, and the calculation temperature is defined as 300K.

[0122] Table 2 HEU-SOL-THERM-027 benchmark test information

[0123]

[0124] The material definition adopts the mass percentage (%) definition method, and fuel is defined as a combustible material. The material mass percentage of the HEU-SOL-THERM-027 benchmark is shown in Table 3.

[0125] Table 3 Material quality ratio of HEU-SOL-THERM-027 benchmark questions

[0126]

[0127] After completing the modeling based on the above information, call the component program to perform calculations and extract the k in the output file. eff The values ​​are compared with the benchmark values, and the accuracy of the core physics multi-group constant library is evaluated based on C / E.

[0128] (2) Fuel consumption benchmark test

[0129] The fuel consumption benchmark test is introduced by taking the SF95-Sample1 benchmark test in SFCOMPO-2 as an example. The fuel of the fuel consumption benchmark test SF95 is UO 2 The fuel cladding is a low-tin Zr-4 alloy. The material composition is shown in Table 4. The outer diameter of the fuel rod cladding is 9.5 mm, the inner diameter is 8.22 mm, and the diameter of the fuel core is 8.05 mm. The core operating pressure is 15.5 MPa, and the coolant inlet and outlet temperatures are 284 ° C and 321 ° C, respectively. A single-grid element calculation model is used to simulate the real SF95 sample. Among them, the outer radius of the cladding is 0.475 cm, the radius of the fuel area is 0.411 cm, the side length of the grid element is 1.265 cm, and the two-dimensional geometric model is as follows Figure 5 The fuel calculation temperature is defined as 900K and the cladding temperature is 600K.

[0130] Table 4 SF95 sample fuel and cladding material information

[0131]

[0132] Moderator materials consider the following elements: 1 H. 16 O. 10 B. 11 B. In actual core operation, the moderator boron concentration changes with the burnup. Therefore, when defining the material, the mass percentage method is used to define the moderator boron concentration at each burnup calculation point. The boron concentration uses the average boron concentration. In the calculation, the burnup value used in each step is defined according to the power change time point given by the SFCOMPO-2.0 database. It is worth noting that at different burnup calculation points, not only are there different burnup values, but the moderator material and power also change accordingly.

[0133] Table 5 Fuel consumption information of SF95-Sample1 at different powers

[0134]

[0135] Based on the above information, the SF95 benchmark problem was modeled and calculated using the component program to obtain the accumulation of each actinide nuclide and fission product nuclide, which was then compared with the corresponding experimental benchmark value to obtain the C / E-1 value. The accuracy of the core physics multi-group constant library was analyzed based on the comparison results.

[0136] Those skilled in the art will readily conceive of other embodiments of the present invention after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses or adaptations of the present invention that follow the general principles of the present invention and include common knowledge or customary techniques in the art that are not disclosed by the present invention. Thus, if these variations and use adaptations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and use adaptations.

[0137] 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 protection of the present invention should be described by the 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 adjusting the resonance integral in a core physics multi-group constant library, characterized in that: The steps include: (S1) determining a descent gradient of a steepest descent method for optimizing a resonance integral for a selected sample experimental group; (S2) determining the optimized and adjusted resonance integral according to the gradient descent direction of the steepest descent method, and merging it into the main library of the target nuclide; (S3) generating subgroup parameters based on the optimized and adjusted resonance integral; (S4) generating an optimized and adjusted core physics multi-group constant library; (S5) Benchmarking the optimized core physics multi-group constant library.

2. The method for adjusting the resonance integral in the core physics multi-group constant library according to claim 1, characterized in that: The method for determining the descent gradient in step (S1) is as follows: First, based on the initial resonance integral RI0, the component calculation program is used to perform transport calculations for the selected sample experimental group to obtain the corresponding integral, and then the initial total chi-square value χ0 is calculated by the integral. 2 , the calculation formula is as follows: Among them, k m is the integral calculated from the mth sample experiment, i.e., the effective multiplication factor; EXP m is the experimental value obtained by measuring the mth sample experiment; Then, by perturbing the resonance integral, the i-th generation resonance integral RI is obtained from formula (2): i , RI i =RI i-1 (1-c i )(2) Among them, RI i is the resonance integral under each background cross section of the i-th generation; RI i-1 is the resonance integral under each background cross section of the i-1th generation; c i is the i-th generation resonance integrated perturbation coefficient; Based on the i-th generation resonance integral RI i For the selected benchmark sample experimental group, the component calculation program is used to perform transport calculations to obtain the corresponding integrals, and then the total chi-square value χ is calculated by the integrals. i 2 ; The descent gradient of the steepest descent method is shown in formula (3): in, is the total chi-square value obtained by the integral calculated by the i-th generation resonance integral; i-1 2 is the total chi-square value obtained by calculating the integral of the i-1th generation resonance integral; c i is the i-th generation resonance integrated perturbation coefficient.

3. The method for adjusting the resonance integral in the core physics multi-group constant library according to claim 2, characterized in that: The objective function of the steepest descent method gradient descent in step (S2) is shown in formula (4): Among them, c i is the i-th generation resonance integral perturbation coefficient; α is the descending step size; is the descending direction; c i+1 is the i+1th generation resonance integrated perturbation coefficient; Then, the optimized and adjusted resonance integral can be obtained through formula (2).

4. The method for adjusting the resonance integral in a core physics multi-group constant library according to any one of claims 1 to 3, characterized in that: In step (S3), a subgroup parameter fitting program is used to obtain optimized subgroup parameters based on the optimized and adjusted resonance integrals through a fitting method.

5. The method for adjusting the resonance integral in the core physics multi-group constant library according to claim 4, characterized in that: The subgroup parameters include two parts: subgroup cross section and subgroup probability.

6. The method for adjusting the resonance integral in a core physics multi-group constant library according to any one of claims 1 to 3, characterized in that: In step (S4), the optimized subgroup parameters are added to the main library file, and the main library of the target nuclide with the subgroup parameters is combined with the main library of other nuclides to generate the optimized core physics multi-group constant library T i+1 , then based on the optimized core physics multi-group constant library T i+1 And the sample experimental group performs reactor physics calculations to obtain the i+1 generation integral. Through optimization iteration, when the total chi-square value of the i+1 generation χ i+1 2 and the total chi-square value of the i-th generation The difference is less than the convergence criterion 1E-5, then the resonance integral that meets the standard and the corresponding core physics multi-group constant library T are obtained. final .

7. The method for adjusting the resonance integral in a core physics multi-group constant library according to any one of claims 1 to 3, characterized in that: In step (S5), the benchmark test includes a criticality benchmark test and a burnup benchmark test; the criticality benchmark test is to select fast spectrum, intermediate energy spectrum, and thermal spectrum benchmark experiments from the International Nuclear Criticality Safety Manual ICSBEP2006 and the Cross-Section Evaluation Working Group Benchmark Experiment Manual ENDF-202 to test the core physics multi-group constant library; the burnup benchmark test is to select a burnup benchmark experiment from the spent fuel isotope composition database SFCOMPO-2, use a component program to perform modeling and calculation, compare the calculation results with the experimental results, and evaluate the accuracy of the burnup calculation.

8. The method for adjusting the resonance integral in a core physics multi-group constant library according to claim 7, characterized in that: The benchmark inspection of the core physics multi-group constant library mainly inspects the key nuclides commonly used in nuclear devices.

9. A system for implementing the method for adjusting the resonance integral in a core physics multi-group constant library as claimed in any one of claims 1 to 8, characterized in that: include: A steepest descent gradient calculation module, used for determining the descent gradient of the steepest descent method for optimizing the resonance integral for the selected sample experimental group; A resonance integral optimization and adjustment module is used to determine the optimized and adjusted resonance integral according to the gradient descent direction of the steepest descent method, and merge it into the main library of the target nuclide; A subgroup parameter making module, based on the optimized and adjusted resonance integral, uses a subgroup parameter fitting program to make subgroup parameters; The core physics multi-group constant library production module generates an optimized and adjusted core physics multi-group constant library based on the optimized sub-group parameters; The core physics multi-group constant library benchmark verification module is used to perform benchmark verification on the optimized core physics multi-group constant library.

10. A device comprising a storage medium and a processor, wherein the storage medium stores a computer program, characterized in that: When the processor executes the computer program, the method for adjusting the resonance integral in the core physics multi-group constant library as described in any one of claims 1 to 8 is implemented.

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