A method for making monte carlo homogenized cross sections suitable for core transport programs

Abstract

The application discloses a method for producing Monte Carlo homogenization cross sections suitable for a reactor core transport program, comprising the following steps: 1, modeling an example and performing continuous energy Monte Carlo transport calculation; 2, tracking neutrons in a specified homogenization region to obtain parameters required for generating basic Monte Carlo homogenization cross sections; 3, generating basic Monte Carlo homogenization cross section data according to step 2; 4, calculating total reaction rates and real spherical harmonic function moments of fluxes in the homogenization region according to step 2; 5, generating high-order total cross section correction terms according to the total reaction rates and the real spherical harmonic function moments of fluxes according to step 4; and 6, updating high-order scattering data according to step 3 and step 5 to form homogenization cross sections suitable for the reactor core transport program.

Description

Technical Field

[0001] This invention relates to the field of particle transport calculation, and in particular to a method for creating a Monte Carlo homogenization cross section suitable for reactor core transport procedures. Background Technology

[0002] To obtain reactor parameters quickly and efficiently, the "two-step method" has become the main approach in reactor engineering. The first step of the "two-step method" is to perform neutron transport calculations on the various structural materials within the reactor core to generate a homogenized cross-section; the second step is to perform multi-group calculations on the reactor core based on the homogenized cross-section generated in the first step to obtain the physical quantities of the reactor core.

[0003] When performing homogenized cross-section generation calculations, deterministic methods inevitably require approximations of indistinguishable resonances and struggle to handle complex geometric systems. The Monte Carlo method, with its advantage of eliminating resonance calculations and its powerful ability to handle complex geometries, becomes an effective means of generating high-precision homogenized cross-sections.

[0004] Currently, the basic Monte Carlo homogenization cross section generation method is based on the conservation of the sum of reactivity in all directions within the homogenization space. This implies that neutrons behave identically in all directions within the homogenization region, meaning the homogenization cross section is independent of neutron direction. However, the homogenization cross section generated by this method cannot guarantee the conservation of reactivity in every direction. Therefore, applying the basic Monte Carlo homogenization cross section to multi-group calculations in reactor core transport procedures can introduce significant errors.

[0005] The Monte Carlo method can track neutrons within a specified direction, thereby generating angle-dependent homogenized cross-section data that reflects the correlation between the homogenized cross-section and its direction. However, this method generates multiple cross-section data for each reaction type in the homogenized region to accommodate neutron simulations in different directions. This results in increased memory consumption of the generated homogenized cross-section data and incompatibility with most reactor core transport solvers.

[0006] Most reactor core transport solvers require cross-sectional data in the same format as the basic Monte Carlo homogenized cross-section data, i.e., homogenized cross-section data independent of neutron direction. The impact of cross-section angle dependence on the calculation is mainly contributed by the total cross-section. To reflect the influence of the total cross-section angle dependence, the deterministic method employs the consistent Pn method (or spherical harmonic moment homogenization technique). This method corrects the influence of the total cross-section angle dependence by expanding the angle-dependent total cross-section and merging the higher-order total cross-section terms into the higher-order scattering matrix. However, the process of solving the correction terms involves the merging of deterministic fine groups and has not yet been applied to the Monte Carlo method. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention provides a Monte Carlo homogenization cross-section fabrication method suitable for reactor core transport procedures. This method is based on spherical harmonic homogenization technology. In continuous energy Monte Carlo calculations, the spherical harmonic moments of the total reaction rate and neutron flux density in the homogenized region are calculated to generate higher-order total cross-section correction terms. Based on the generated basic homogenized cross-section data, the higher-order scattering matrix is ​​updated to form homogenized cross-section data suitable for transport procedures. By statistically analyzing the spherical harmonic moments of the total reaction rate and neutron flux density within the homogenized region, the calculation of higher-order total cross-section correction terms and the correction of the higher-order scattering matrix are realized. This allows the new homogenized cross-section data to reflect the angular correlation of the total cross-section while retaining the same data format as the basic Monte Carlo homogenized cross-section data, thus improving the accuracy of the homogenized cross-section in reactor core transport calculations.

[0008] To achieve the aforementioned objectives of the invention, the technical solution adopted to solve its technical problems is as follows:

[0009] A method for fabricating a Monte Carlo homogenization cross section suitable for reactor core transport procedures includes the following steps:

[0010] Step 1: Model the example and perform continuous energy Monte Carlo transport calculations;

[0011] Step 2: Track neutrons within the specified homogenization region to obtain the parameters required for generating the basic Monte Carlo homogenization cross section;

[0012] Step 3: Based on Step 2, generate basic Monte Carlo homogenized section data;

[0013] Step 4: Based on Step 2, calculate the real spherical harmonic moments of the total reaction rate and flux within the homogenized region;

[0014] Step 5: Based on Step 4, generate a higher-order total cross-section correction term according to the real spherical harmonic moments of the total reaction rate and flux;

[0015] Step 6: Based on Step 3 and Step 5, update the higher-order scattering data to form a homogenized cross section suitable for the core transport process.

[0016] Furthermore, step 3 includes:

[0017] Based on the various reaction rates, neutron flux, intergroup transition probabilities, and other parameters calculated in step 2, the basic Monte Carlo homogenized reaction cross section data are obtained by formula (1), and the basic Monte Carlo homogenized scattering and higher-order scattering matrix data are obtained by formula (2), thus forming the basic Monte Carlo homogenized cross section data:

[0018]

[0019]

[0020] in:

[0021] The homogenization region k generated by the basic Monte Carlo homogenization method and the x-type reaction cross section within the energy group G;

[0022] The first-order intergroup transfer cross section, representing the scattering from energy group G' to energy group G within the homogenized region k produced by the basic Monte Carlo homogenization method;

[0023] The reaction rate of type x within the homogenized region k and energy group G is obtained in step 2; The neutron standard flux representing the homogenized region k and energy group G is obtained in step 2;

[0024] The scattering response rate, representing the homogenization region k and the energy group G', is obtained in step 2;

[0025] f G′→G，l The l-th Legendre moment, representing the angle-related probability that the energy of a neutron in energy group G' falls into group G after a scattering reaction, is obtained in step 2.

[0026] G represents the energy group number;

[0027] G' represents the energy group number;

[0028] k represents the fine structure number;

[0029] x represents the reaction type;

[0030] t represents the overall reaction;

[0031] s represents the scattering reaction;

[0032] l represents the order of the Legendre polynomial.

[0033] Furthermore, step 4 includes:

[0034] Based on the calculation described in step 2, neutrons within the specified homogenization region are tracked. In the continuous energy Monte Carlo transport calculation, the real spherical harmonic moment of the total reaction rate in the homogenization region is calculated using formula (3), and the real spherical harmonic moment of the neutron flux in the homogenization region is calculated using formula (4):

[0035]

[0036]

[0037] in:

[0038] The m-th term of the l-th spherical harmonic moment of the neutron flux density within the homogenized region k and energy group G;

[0039] The m-th term of the first-order spherical harmonic moment representing the total reaction rate within the range of fine structure k and energy group G;

[0040] The neutron angular flux density represents the neutron direction Ω within the fine structure k and energy group G.

[0041] The total reaction rate with the neutron direction Ω within the homogenization region k and energy group G;

[0042] Y l，m (Ω) represents the m-th term of the first-order real spherical harmonic function;

[0043] k represents the fine structure number;

[0044] G represents the energy group number;

[0045] Ω represents the direction of neutrons;

[0046] l represents the order of the Legendre polynomial;

[0047] m represents the number of real spherical harmonic terms;

[0048] t represents the overall reaction.

[0049] Furthermore, step 5 includes:

[0050] Based on the real spherical harmonic moments of the reaction rate and flux in each homogenized region obtained in step 4, the higher-order total cross-section correction term is calculated using formula (5):

[0051]

[0052] in:

[0053] The l-th order total cross section correction term represents the homogenized region A and the energy group G.

[0054] Furthermore, step 6 includes:

[0055] Based on the basic Monte Carlo homogenization cross section data obtained in step 3 and the higher-order total cross section correction term obtained in step 5, the higher-order scattering matrix data is updated using formula (6) to form a Monte Carlo homogenization cross section suitable for the core transport process:

[0056]

[0057] in:

[0058] This represents the first-order intergroup transfer cross section within the updated homogenized region k, from energy group G' to energy group G.

[0059] The first-order intergroup transfer cross section, representing the scattering from energy group G' to energy group G within the homogenized region k produced by the basic Monte Carlo homogenization method;

[0060] The homogenization region k produced by the basic Monte Carlo homogenization method and the total cross section within the energy group G represent the homogenization region k and the total cross section within the energy group G.

[0061] δ represents the Dirac function;

[0062] s represents the scattering reaction;

[0063] G' represents the energy group number.

[0064] Furthermore, in step 6, based on steps 3 and 5, a Monte Carlo homogenization cross section suitable for the core transport process is generated, including the spherical harmonic function moments of the total reaction rate and neutron flux calculated in step 4 and the homogenization cross section data obtained in step 3, to generate a Monte Carlo homogenization cross section suitable for the core transport process.

[0065] By employing the above technical solutions, this invention has the following advantages and positive effects compared with the prior art:

[0066] 1. This invention considers the angular correlation of the total cross section when generating a homogenized cross section, which can produce higher accuracy when applied to the core transport process;

[0067] 2. The homogenized cross-section data format generated by this invention is the same as the basic homogenized cross-section data, and it has strong adaptability to different core transport procedures;

[0068] 3. This invention improves upon the Monte Carlo method for generating homogenized cross sections, while retaining the cross section accuracy gained from the Monte Carlo method's ability to eliminate the need for resonance approximation and complex geometric processing.

[0069] 4. This invention uses spherical harmonic moment homogenization technology to correct the angular correlation of the total cross section in the homogenized cross section to a higher-order scattering matrix. This allows the cross section database to reflect the angular correlation of the total cross section while maintaining the format that the total cross section is independent of the angle, thereby improving the accuracy of the results of homogenized cross sections used for multi-group transport calculations. Attached Figure Description

[0070] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0071] Figure 1 This is a schematic flowchart of a method for fabricating a Monte Carlo homogenization cross section applicable to reactor core transport procedures according to the present invention. Detailed Implementation

[0072] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] like Figure 1 As shown, this embodiment discloses a method for fabricating a Monte Carlo homogenization cross section suitable for reactor core transport procedures, including the following steps:

[0074] Step 1: Model the example and perform continuous energy Monte Carlo transport calculations;

[0075] Specifically, for the computational examples required, a detailed geometric model is performed using the voxel construction method to rigorously and accurately characterize the geometric structure of the examples. Based on the established geometric model, continuous-energy Monte Carlo neutron transport calculations are then performed.

[0076] Step 2: Track neutrons within the specified homogenization region to obtain the parameters required for generating the basic Monte Carlo homogenization cross section;

[0077] Specifically, based on the calculations described in step 1, neutrons within the specified homogenization region are tracked. For the specified homogenization space, the behavior of neutrons within the homogenization region is statistically analyzed to obtain the basic physical parameters required for generating the Monte Carlo homogenization cross section, such as various reaction rates, neutron flux density, fission fraction, and inter-swarm transfer probability. The various reaction rates include total reaction rate, absorption rate, scattering reaction rate, and fission reaction rate.

[0078] Step 3: Based on Step 2, generate basic Monte Carlo homogenized section data;

[0079] Specifically, step 3 includes:

[0080] Based on the various reaction rates, neutron flux, intergroup transition probabilities, and other parameters calculated in step 2, the basic Monte Carlo homogenized reaction cross section data are obtained by formula (1), and the basic Monte Carlo homogenized scattering and higher-order scattering matrix data are obtained by formula (2), thus forming the basic Monte Carlo homogenized cross section data:

[0081]

[0082]

[0083] in:

[0084] The homogenization region k generated by the basic Monte Carlo homogenization method and the x-type reaction cross section within the energy group G;

[0085] The l-th order intergroup transfer cross section, representing the scattering from energy group G' to energy group G within the homogenized region k produced by the basic Monte Carlo homogenization method;

[0086] The reaction rate of type x within the homogenized region k and energy group G is obtained in step 2; The neutron standard flux representing the homogenized region k and energy group G is obtained in step 2;

[0087] The scattering response rate, representing the homogenization region k and the energy group G', is obtained in step 2;

[0088] f G′→G，l The l-th Legendre moment, representing the angle-related probability that the energy of a neutron in energy group G' falls into group G after a scattering reaction, is obtained in step 2.

[0089] G represents the energy group number;

[0090] G' represents the energy group number;

[0091] k represents the fine structure number;

[0092] x represents the reaction type;

[0093] t represents the overall reaction;

[0094] s represents the scattering reaction;

[0095] l represents the order of the Legendre polynomial.

[0096] Step 4: Based on Step 2, calculate the real spherical harmonic moments of the total reaction rate and flux within the homogenized region;

[0097] Specifically, step 4 includes:

[0098] Based on the calculation described in step 2, neutrons within the specified homogenization region are tracked. In the continuous energy Monte Carlo transport calculation, the real spherical harmonic moment of the total reaction rate in the homogenization region is calculated using formula (3), and the real spherical harmonic moment of the neutron flux in the homogenization region is calculated using formula (4):

[0099]

[0100]

[0101] in:

[0102] The m-th term of the first-order spherical harmonic moment of the neutron flux density within the homogenized region k and energy group G;

[0103] The m-th term of the first-order spherical harmonic moment representing the total reaction rate within the range of fine structure k and energy group G;

[0104] The neutron angular flux density represents the neutron direction Ω within the fine structure k and energy group G.

[0105] The total reaction rate with the neutron direction Ω within the homogenization region k and energy group G;

[0106] Y l，m (Ω) represents the m-th term of the first-order real spherical harmonic function;

[0107] k represents the fine structure number;

[0108] G represents the energy group number;

[0109] Ω represents the direction of neutrons;

[0110] l represents the order of the Legendre polynomial;

[0111] m represents the number of real spherical harmonic terms;

[0112] t represents the overall reaction.

[0113] Step 5: Based on Step 4, generate a higher-order total cross-section correction term according to the real spherical harmonic moments of the total reaction rate and flux;

[0114] Specifically, step 5 includes:

[0115] Based on the real spherical harmonic moments of the reaction rate and flux in each homogenized region obtained in step 4, the higher-order total cross-section correction term is calculated using formula (5):

[0116]

[0117] in:

[0118] The first-order total cross-section correction term represents the homogenization region A and the energy group G.

[0119] Step 6: Based on Step 3 and Step 5, update the higher-order scattering data to form a homogenized cross section suitable for the core transport process.

[0120] Specifically, step 6 includes:

[0121] Based on the basic Monte Carlo homogenization cross section data obtained in step 3 and the higher-order total cross section correction term obtained in step 5, the higher-order scattering matrix data is updated using formula (6) to form a Monte Carlo homogenization cross section suitable for the core transport process:

[0122]

[0123] in:

[0124] This represents the first-order intergroup transfer cross section within the updated homogenized region k, from energy group G' to energy group G.

[0125] The first-order intergroup transfer cross section, representing the scattering from energy group G' to energy group G within the homogenized region k produced by the basic Monte Carlo homogenization method;

[0126] The homogenization region k produced by the basic Monte Carlo homogenization method and the total cross section within the energy group G represent the homogenization region k and the total cross section within the energy group G.

[0127] δ represents the Dirac function;

[0128] s represents the scattering reaction;

[0129] G' represents the energy group number.

[0130] Furthermore, in step 6, based on steps 3 and 5, a Monte Carlo homogenization cross section suitable for the core transport process is generated, including the spherical harmonic function moments of the total reaction rate and neutron flux calculated in step 4 and the homogenization cross section data obtained in step 3, to generate a Monte Carlo homogenization cross section suitable for the core transport process.

[0131] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for fabricating a Monte Carlo homogenization cross section suitable for reactor core transport procedures, characterized in that, Includes the following steps: Step 1: Model the example and perform continuous energy Monte Carlo transport calculations; Step 2: Track neutrons within the specified homogenization region to obtain the parameters required for generating the basic Monte Carlo homogenization cross section; Step 3: Based on Step 2, generate basic Monte Carlo homogenized section data; Step 3 includes: Based on the various reaction rates, neutron fluxes, and intergroup transfer probability parameters calculated in step 2, the basic Monte Carlo homogenized reaction cross section data are obtained by formula (1), and the basic Monte Carlo homogenized scattering and higher-order scattering matrix data are obtained by formula (2), thus forming the basic Monte Carlo homogenized cross section data: Official (1) Official (2) in: The homogenization region k generated by the basic Monte Carlo homogenization method and the x-type reaction cross section within the energy group G; The l-th order intergroup transfer cross section, representing the scattering from energy group G' to energy group G within the homogenized region k produced by the basic Monte Carlo homogenization method; The reaction rate of type x within the homogenized region k and energy group G is obtained in step 2; The neutron standard flux representing the homogenized region k and energy group G is obtained in step 2; The scattering response rate, representing the homogenization region k and the energy group G', is obtained in step 2; The l-th Legendre moment, representing the angle-related probability that the energy of a neutron in energy group G' falls into group G after a scattering reaction, is obtained in step 2. G represents the energy group number; G' represents the energy group number; k represents the fine structure number; x represents the reaction type; t represents the overall reaction; s represents the scattering reaction; l represents the order of the Legendre polynomial; Step 4: Based on Step 2, calculate the real spherical harmonic moments of the total reaction rate and flux within the homogenized region; Step 5: Based on Step 4, generate a higher-order total cross-section correction term according to the real spherical harmonic moments of the total reaction rate and flux; Step 6: Based on Step 3 and Step 5, update the higher-order scattering data to form a homogenized cross section suitable for the core transport process.

2. The method for fabricating a Monte Carlo homogenization cross section suitable for reactor core transport procedures according to claim 1, characterized in that, Step 4 includes: Based on the calculation described in step 2, neutrons within the specified homogenization region are tracked. In the continuous energy Monte Carlo transport calculation, the real spherical harmonic moment of the total reaction rate in the homogenization region is calculated using formula (3), and the real spherical harmonic moment of the neutron flux in the homogenization region is calculated using formula (4): Official (3) Official (4) in: The m-th term of the l-th spherical harmonic moment of the neutron flux density within the homogenized region k and energy group G; The m-th term of the l-th spherical harmonic moment representing the total reaction rate within the range of fine structure k and energy group G; Representing the fine structure k and the energy group G, the neutron direction is... neutron angular flux density; The neutron direction is within the homogenization region k and energy group G. The overall reaction rate; This represents the m-th term of the l-th order real spherical harmonic function; k represents the fine structure number; G represents the energy group number; Represents the direction of neutrons; l represents the order of the Legendre polynomial; m represents the number of real spherical harmonic terms; t represents the overall reaction.

3. The method for fabricating a Monte Carlo homogenization section suitable for reactor core transport procedures according to claim 2, characterized in that, Step 5 includes: Based on the real spherical harmonic moments of the reaction rate and flux in each homogenized region obtained in step 4, the higher-order total cross-section correction term is calculated using formula (5): Official (5) in: The l-th order total cross section correction term represents the homogenized region A and the energy group G.

4. The method for fabricating a Monte Carlo homogenization cross section suitable for reactor core transport procedures according to claim 3, characterized in that, Step 6 includes: Based on the basic Monte Carlo homogenization cross section data obtained in step 3 and the higher-order total cross section correction term obtained in step 5, the higher-order scattering matrix data is updated using formula (6) to form a Monte Carlo homogenization cross section suitable for the core transport process: Official (6) in: The l-th order intergroup transfer cross section represents the scattering from energy group G' to energy group G within the updated homogenized region k. The l-th order intergroup transfer cross section, representing the scattering from energy group G' to energy group G within the homogenized region k produced by the basic Monte Carlo homogenization method; The homogenization region k produced by the basic Monte Carlo homogenization method and the total cross section within the energy group G represent the homogenization region k and the total cross section within the energy group G. Represents the Dirac function; s represents the scattering reaction; G' represents the energy group number.

5. The method for fabricating a Monte Carlo homogenization cross section suitable for reactor core transport procedures according to claim 4, characterized in that, In step 6, based on steps 3 and 5, a Monte Carlo homogenization cross section suitable for the reactor core transport process is generated. This includes the spherical harmonic moment of the calculated total reaction rate and neutron flux in step 4 and the homogenization cross section data obtained in step 3, thereby generating a Monte Carlo homogenization cross section suitable for the reactor core transport process.

Images