Neutron energy spectrum analysis method based on energy response

Abstract

A neutron energy spectrum analysis method based on energy response comprises the steps that after an energy response matrix of a target piece material is generated according to nuclide proportion weighting, modeling is conducted on a fuel rod area, an obtained average collision probability matrix serves as an interpolation factor, interpolation is conducted on incident neutron energy distribution when the internal cross section of a fuel rod model is 0 and infinity, and a neutron energy spectrum analysis result is obtained; obtaining incident neutron energy distribution; performing matrix multiplication on the incident neutron energy distribution, the energy response matrix of the target material and the average collision probability matrix to obtain neutron energy distribution after one-time collision, and updating the incident neutron energy distribution as one-time collision simulation; and after multiple collision simulations are performed until the incident neutron energy distribution is stable, dividing each element by the total cross section of the corresponding energy group to obtain a neutron energy spectrum. According to the method, the response relation of nuclides to energy is processed into the response matrix by analyzing the nuclear database, the neutron energy spectrum is rapidly analyzed through iteration of the initial source item and the response matrix, and accurate analysis of the high-resolution neutron energy spectrum is efficiently achieved.

Description

Technical Field

[0001] The invention relates to a technology in the field of nuclear reactor design, in particular to a neutron energy spectrum rapid analysis method based on energy response. Background Art

[0002] Existing neutron spectrum analysis methods usually use deterministic or probabilistic methods to directly simulate neutron transport, and then construct neutron spectrum by counting the neutron flux of each energy group under specific energy group division. Deterministic methods introduce a lot of approximations to geometry and materials, resulting in inaccurate results. Probabilistic methods are inefficient and difficult to accurately obtain neutron spectrum with high energy spectrum resolution due to statistical errors. As a result, existing neutron spectrum simulation technology cannot directly obtain neutron spectrum through simulation without the help of detectors. Summary of the invention

[0003] In view of the problems of low computational efficiency and low energy spectrum resolution of existing neutron energy spectrum analysis methods, the present invention proposes a neutron energy spectrum analysis method based on energy response. By analyzing the nuclear database, the response relationship of nuclides to energy is processed into a response matrix, and the neutron energy spectrum is quickly analyzed by iteratively performing initial source terms and response matrices, thereby efficiently achieving accurate analysis of high-resolution neutron energy spectrum.

[0004] The present invention is achieved through the following technical solutions:

[0005] The invention relates to a neutron spectrum analysis method based on energy response. After the energy response matrix of a target material is generated by weighting according to the nuclide ratio, a fuel rod region is modeled and an average collision probability matrix is ​​obtained as an interpolation factor. The incident neutron energy distribution when the internal cross section of the fuel rod model is 0 and infinite is interpolated to obtain the incident neutron energy distribution; then, the incident neutron energy distribution, the energy response matrix of the target material and the average collision probability matrix are subjected to matrix multiplication operation to obtain the neutron energy distribution after one collision and update the incident neutron energy distribution as a collision simulation; after multiple collision simulations until the incident neutron energy distribution is stable, each element thereof is divided by the total cross section of the corresponding energy group to obtain the neutron energy spectrum.

[0006] The nuclide ratio weighting mentioned above means: dividing the full energy zone into n energy groups, using the Monte Carlo method to randomly sample a large number of particles from the ACE database of all nuclides, calculating the energy transfer of each particle, normalizing the statistical average of the energy transfer of all particles to a probability of 1 and storing it in a matrix to generate an energy response matrix of the nuclides; and then weighting the energy response matrix of the nuclides according to the nuclide composition of the target material and taking the collision probability of the nuclides and neutrons as weights to generate the energy response matrix R of the material. mat .

[0007] The collision probability of the nuclide and the neutron Where: f k，i is the probability of nuclide k colliding with neutrons in the i-th energy group, N k is the atomic density of nuclide k in the material, is the total microscopic cross section of nuclide k in the ith energy group, read from the ACE database, is the total macroscopic cross section of the material in the i-th energy group.

[0008] The average collision probability matrix P is obtained by randomly sampling particles in the model of the fuel rod region constructed using constructive solid geometry, and calculating the distance from each particle to the region boundary respectively, and calculating the average collision probability according to the exponential decay law. n×n , where: n is the total number of energy groups divided, the elements on the diagonal of the i-th row of the matrix Where: p i is the average collision probability of neutrons in the i-th energy group, and b is the distance from the neutron to the boundary.

[0009] The average collision probability matrix is ​​an n×n diagonal matrix.

[0010] The incident neutron energy distribution is calculated by changing the macroscopic total cross section of the fuel rod area to 0 and positive infinity, and using the Monte Carlo method to calculate the neutron energy distribution of two incidents on the fuel rod area. and Then, the average collision probability matrix is ​​used as the interpolation factor. and Interpolate between to obtain the neutron energy distribution incident on the fuel rod area

[0011] The primary collision simulation refers to: the energy distribution of incident neutrons Material response matrix and average collision probability matrix P n×n Perform matrix multiplication to obtain the neutron energy distribution after one collision The incident neutron energy distribution Supplementary vector To probability 1 as an update, specifically: due to nuclide absorption effect and geometric leakage, The sum of the elements of the vector s is less than 1, the initial source of the next iteration

[0012] The incident neutron energy distribution is stable, which means that after multiple collision simulations, the incident neutron energy distribution is Energy distribution of the m+1th incident neutron The relative deviation of each corresponding element in is less than 1×10 -6 , where: m is the number of simulations.

[0013] The present invention relates to a system for realizing the above method, comprising: a response matrix unit, a collision probability unit, an incident source term unit and a matrix operation unit, wherein: the response matrix unit performs random sampling calculation of the statistical average of various nuclide energy transfers according to an ACE database to obtain an energy response matrix of each nuclide; the collision probability unit calculates the average collision probability of a large number of particles according to the geometric material information of the fuel rod area according to the exponential decay law to obtain an average collision probability matrix; the incident source term unit performs statistics on the neutron energy distribution when the macroscopic total cross-section of the fuel rod area is 0 and positive infinity according to the geometric distribution of the fuel rod area, and interpolates the incident neutron energy distribution using the average collision probability matrix as an interpolation factor; the matrix operation unit iteratively performs matrix multiplication calculation according to the information of the response matrix unit, the collision probability unit and the incident source term unit to obtain a final neutron energy spectrum. Technical Effects

[0014] The present invention generates the energy response matrix of the nuclide based on the ACE database, models the fuel rod area using constructive solid geometry, obtains the average collision probability matrix and incident neutron energy distribution, and then quickly analyzes the neutron energy spectrum through matrix calculation. Compared with the prior art, the present invention reduces the introduction of approximation, ensures high accuracy, significantly improves the calculation efficiency, and avoids the decrease in energy spectrum accuracy caused by statistical errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of the present invention;

[0016] Figure 2 This is a schematic diagram of the fuel rod area of ​​an embodiment;

[0017] Figure 3 is the incident neutron energy distribution diagram of the fuel rod;

[0018] Figure 4 This is the neutron spectrum of the air filling the fuel rods;

[0019] Figure 5 This is the neutron spectrum of boron-water filled fuel rods;

[0020] Figure 6 This is the neutron spectrum of uranium dioxide filled in the fuel rod;

[0021] Figure 7 Neutron spectrum of stainless steel filling the fuel rods. DETAILED DESCRIPTION

[0022] This embodiment uses Figure 2 Take the energy spectrum analysis problem of four commonly used materials in various nuclear reactors: air, boron water, uranium dioxide and stainless steel in the pressurized water reactor fuel assembly shown in the figure as an example. Figure 1As shown, the implementation method of the neutron spectrum analysis technology based on energy response involved in this embodiment specifically includes:

[0023] Step 1: Read the nuclide energy response matrix and the incident neutron energy distribution when the internal cross section of the fuel rod is 0 and ∞.

[0024] Step 2: Weight the nuclide energy response matrix by the nuclide ratio of each material to calculate the energy response matrix R of the target material. mat .

[0025] Step 3: Model the fuel rod area and calculate the average collision probability matrix P through random sampling.

[0026] Step 4: Using the collision probability matrix as the interpolation factor, interpolate the incident neutron energy distribution when the internal cross section of the fuel rod is 0 and ∞ to obtain the incident neutron energy distribution like Figure 3 shown.

[0027] Step 5: Perform matrix multiplication on the material's energy response matrix, incident neutron energy distribution, and average collision probability, and iterate until the neutron energy distribution converges.

[0028] Step 6: Divide the neutron energy distribution vector by the macroscopic total cross section of the energy group and normalize it to obtain the neutron energy spectrum.

[0029] After specific experiments, the Monte Carlo method was used to verify the neutron spectrum obtained by this method. The neutron spectrum comparison results of four materials, air, boron water, uranium dioxide and stainless steel, are as follows: Figures 4 to 7 As shown in the figure, the red curve is the neutron energy spectrum obtained by the present invention, and the blue area is the 3σ area of ​​the Monte Carlo method. The more the red curve falls in the blue area, the more accurate the calculation result is.

[0030] In this embodiment, a detailed comparison of the verification neutron spectrum results is shown in Table 1, which shows the detailed results of the neutron spectrum of each material obtained by the technology of the present invention and the Monte Carlo method. A comparison table of the verified qualitative calculation effect is shown in Table 2, which includes the percentage of the neutron spectrum of each material of the present invention in the Monte Carlo 3σ region, the root mean square error of the neutron spectrum of each material compared to the Monte Carlo result, and the calculation time of the two methods.

[0031] Table 1. Comparison of the results of this embodiment and Monte Carlo neutron spectroscopy

[0032] Table 2. Comparison of the results of this embodiment and Monte Carlo calculation

[0033] As can be seen from Table 2, the neutron energy spectra obtained by all the test materials of the present invention are within the 3σ region of the Monte Carlo method by more than 90%, and the root mean square error is kept within 10 -4 Therefore, the technology of the present invention has a very high calculation accuracy, and the calculation time of the present invention is in the order of seconds, which is much lower than the Monte Carlo method.

[0034] Compared with the neutron spectrum analysis method based on determinism, the present invention uses constructive solid geometry to model a specific area, and generates the energy response relationship of nuclides based on the ACE database, which reduces the introduction of approximations and ensures the high accuracy of the results. Compared with the neutron spectrum analysis method based on probability theory, this method uses matrix operations to obtain the neutron spectrum, has high computational efficiency and avoids the decrease in spectrum accuracy due to statistical errors. The present invention effectively improves the efficiency and spectrum resolution of neutron spectrum analysis, and provides technical support for the design of nuclear reactor systems.

[0035] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A neutron spectrum analysis method based on energy response, It is characterized in that After the energy response matrix of the target material is generated by weighting the nuclide ratio, the fuel rod area is modeled and the average collision probability matrix is ​​used as the interpolation factor to interpolate the incident neutron energy distribution when the internal cross-section of the fuel rod model is 0 and infinite to obtain the incident neutron energy distribution; the incident neutron energy distribution, the energy response matrix of the target material and the average collision probability matrix are then matrix multiplied to obtain the neutron energy distribution after one collision and update the incident neutron energy distribution as a collision simulation; after multiple collision simulations until the incident neutron energy distribution is stable, each element is divided by the total cross-section of the corresponding energy group to obtain the neutron energy spectrum.

2. The neutron spectrum analysis method based on energy response according to claim 1, Its characteristics are: The nuclide ratio weighting means: dividing the full energy zone into n energy groups, using the Monte Carlo method to randomly sample a large number of particles from the ACE database of all nuclides, calculating the energy transfer of each particle, normalizing the statistical average of the energy transfer of all particles to a probability of 1 and storing it in a matrix, and generating an energy response matrix of the nuclides; Then, according to the nuclide composition of the target material, the energy response matrix of the nuclide is weighted with the collision probability of the nuclide and the neutron as the weight to generate the energy response matrix R of the material. mat ; The collision probability of the nuclide and the neutron Where: f k，i is the probability of nuclide k colliding with neutrons in the i-th energy group, N k is the atomic density of nuclide k in the material, is the total microscopic cross section of nuclide k in the ith energy group, read from the ACE database, is the total macroscopic cross section of the material in the i-th energy group.

3. The neutron spectrum analysis method based on energy response according to claim 1, Its characteristics are: The average collision probability matrix P is obtained by randomly sampling particles in the model of the fuel rod region constructed using constructive solid geometry, and calculating the distance from each particle to the region boundary respectively, and calculating the average collision probability according to the exponential decay law. n×n , where: n is the total number of energy groups divided, the elements on the diagonal of the i-th row of the matrix Where: p i is the average collision probability of neutrons in the i-th energy group, and b is the distance from the neutron to the boundary.

4. The neutron spectrum analysis method based on energy response according to claim 1 or 3, Its characteristics are: The incident neutron energy distribution is calculated by changing the macroscopic total cross section of the fuel rod area to 0 and positive infinity, and using the Monte Carlo method to calculate the neutron energy distribution of two incidents on the fuel rod area. and Then, the average collision probability matrix is ​​used as the interpolation factor. and Interpolate between to obtain the neutron energy distribution incident on the fuel rod area 5. The neutron spectrum analysis method based on energy response according to claim 1, Its characteristics are: The primary collision simulation refers to: the energy distribution of incident neutrons Material response matrix and average collision probability matrix P n×n Perform matrix multiplication to obtain the neutron energy distribution after one collision The incident neutron energy distribution Supplementary vector To probability 1 as an update, specifically: due to nuclide absorption effect and geometric leakage, The sum of the elements of the vector s is less than 1, the initial source of the next iteration 6. The neutron spectrum analysis method based on energy response according to claim 1, Its characteristics are: The incident neutron energy distribution is stable, which means that after multiple collision simulations, the incident neutron energy distribution is Energy distribution of the m+1th incident neutron The relative deviation of each corresponding element in is less than 1×10 -6 , where: m is the number of simulations.

7. The neutron spectrum analysis method based on energy response according to any one of claims 1 to 6, Its characteristics are: Specifically include: Energy spectrum analysis of air, boric water, uranium dioxide and stainless steel, including: Step 1, read the nuclide energy response matrix and the incident neutron energy distribution when the internal cross section of the fuel rod is 0 and ∞; Step 2: Weight the nuclide energy response matrix by the nuclide ratio of each material to calculate the energy response matrix R of the target material. mat ; Step 3: Model the fuel rod area and calculate the average collision probability matrix P by random sampling; Step 4: Using the collision probability matrix as the interpolation factor, interpolate the incident neutron energy distribution when the internal cross section of the fuel rod is 0 and ∞ to obtain the incident neutron energy distribution Step 5, perform matrix multiplication on the material energy response matrix, incident neutron energy distribution and average collision probability, and iterate until the neutron energy distribution converges; Step 6: Divide the neutron energy distribution vector by the macroscopic total cross section of the energy group and normalize it to obtain the neutron energy spectrum.

8. A neutron spectrum analysis system based on energy response for implementing any of the methods described in claims 1 to 7, It is characterized in that include: A response matrix unit, a collision probability unit, an incident source term unit and a matrix operation unit, wherein: the response matrix unit calculates the statistical average of energy transfer of various nuclides by random sampling according to the ACE database to obtain the energy response matrix of each nuclide; The collision probability unit calculates the average collision probability of a large number of particles according to the geometric material information of the fuel rod area using the exponential decay law to obtain the average collision probability matrix; the incident source term unit calculates the neutron energy distribution when the macroscopic total cross-section of the fuel rod area is 0 and positive infinity according to the geometric distribution of the fuel rod area, and interpolates the incident neutron energy distribution using the average collision probability matrix as the interpolation factor; the matrix operation unit iteratively performs matrix multiplication operations based on the information of the response matrix unit, the collision probability unit, and the incident source term unit to obtain the final neutron energy spectrum.

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