Iterative power reactor neutron noise analysis method based on Monte Carlo method

Abstract

The invention discloses an iterative dynamic reactor neutron noise analysis method based on a Monte Carlo method. The method comprises the following steps: 1, establishing a three-dimensional model containing reactor core geometry, material parameters and disturbance parameters; 2, neutron noise source items are determined through Monte Carlo critical calculation; 3, deriving an iteration format based on a noise equation; 4, sampling initial source particle distribution according to the noise source item obtained in the step 2, and entering iteration; 5, storing instant fission neutrons into a fission library in each generation of circulation, and directly treating delayed neutrons by using secondary particles; dynamically updating ks values and source distribution according to the fission library and noise source items; and 6, counting neutron noise space distribution characteristics after multi-generation iteration convergence. According to the method, neutron noise analysis is carried out by adopting the Monte Carlo method, approximation is less, geometric modeling is flexible, and a high-precision reference solution can be provided; through fusion of an iterative algorithm, the calculation efficiency and stability are improved, and reliable support is provided for nuclear reactor core monitoring, fault diagnosis and noise analysis software development.

Description

Technical Field

[0001] The present invention belongs to the fields of power reactor neutron noise calculation and particle transport calculation in nuclear reactor physics calculation, and particularly relates to an iterative power reactor neutron noise analysis method based on the Monte Carlo method. Background Art

[0002] Reactor neutron noise refers to the fluctuation of the neutron flux density in the reactor around its average value during steady-state operation. Neutron noise carries a large amount of information about the operation of the nuclear reactor. Analyzing reactor neutron noise is of great significance for reactor core operation condition monitoring and fault diagnosis, etc. In a power reactor, the induction of neutron noise mainly depends on the core parameter fluctuations caused by macroscopic processes in the nuclear reactor, such as core component vibration, moderator temperature or density perturbation, etc. The main advantage of the reactor online diagnosis and monitoring system based on neutron noise is non-invasive, and it can detect possible abnormal phenomena using current out-of-core and in-core detectors.

[0003] Simulating the generation of neutron noise and its transport process in the core can provide a basis for the operation and optimization of the reactor core and the development of a non-invasive core online monitoring system. With the development of artificial intelligence and machine learning methods in recent years, classifying and locating various noise sources is a very promising research direction. Therefore, the numerical simulation of neutron noise has also become a key research direction.

[0004] The existing applications of neutron noise transport simulation are few, and mainly focus on using deterministic methods for transport solution. In contrast, the neutron noise simulation based on the Monte Carlo method has the characteristics of fewer theoretical approximations, high geometric modeling accuracy, wide applicability to special reactor types, and can provide a high-precision reference solution for other methods.

[0005] The traditional Monte Carlo method uses a direct simulation method, which requires simulating a large number of particle histories, resulting in very time-consuming calculations. Using the iterative format proposed in the present invention to transform the original formula can effectively accelerate the simulation, avoid the complete simulation of long particle histories, and significantly improve the calculation efficiency. Summary of the Invention

[0006] To overcome the problems of poor calculation stability, low efficiency, and huge calculation amount in the traditional Monte Carlo method for solving neutron noise problems, the purpose of the present invention is to provide an iterative power reactor neutron noise analysis method based on the Monte Carlo method. Based on the characteristics of the Monte Carlo method, the present invention improves the traditional neutron noise equation and constructs an iterative format, which can effectively accelerate the simulation, avoid the complete simulation of long particle histories, improve the calculation stability, and increase the calculation efficiency.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] An iterative power reactor neutron noise analysis method based on the Monte Carlo method, comprising the following steps:

[0009] Step 1. Accurately model and describe the spatial geometry composition and material components of the core of the target power reactor, and at the calculation frequency point, accurately model and describe the spatial position, perturbation cross-section and phase of the perturbation material source;

[0010] Step 2. Use the critical calculation mode of the Monte Carlo method, set the statistical active generation, and after reaching the statistical active generation, calculate the neutron noise source term at the calculation frequency point;

[0011] Step 3. Reconstruct and deform the traditional neutron noise equation to construct an iterative format of the Monte Carlo method;

[0012] Step 4. According to the neutron noise source term calculated in Step 2, sample the initial noise source particle distribution, and start the Monte Carlo iterative loop calculation according to the iterative format;

[0013] Step 5. In the core of the target power reactor, perform neutron noise transport calculation, store the generated prompt fission neutrons in the fission library, and simulate the delayed fission neutrons using secondary particles; after all the particles in this generation are simulated, update the scaling factor k s,n and the noise source particle distribution, and construct a new generation of source distribution according to the fission library and the noise source term;

[0014] Step 6. When the set maximum number of iterations is reached, enter the statistical active generation, perform statistical averaging and result normalization on the statistical active generation to obtain the average scaling factor k s,avg and the neutron noise spatial distribution characteristics.

[0015] Compared with the prior art, the present invention has the following outstanding advantages:

[0016] 1) Compared with the deterministic method, this method has fewer geometric approximations and fewer theoretical approximations, so it has the characteristic of accurate calculation;

[0017] 2) Compared with the traditional Monte Carlo method, using the improved Monte Carlo iterative format for calculation, there is no need to fully simulate the long particle history containing all fission secondary particles, which ensures the accuracy while improving the calculation efficiency;

[0018] In summary, the method of the present invention provides a new paradigm for the calculation of neutron noise on the premise of ensuring the calculation accuracy, and improves the efficiency of calculating neutron noise by the Monte Carlo method. Description of the Drawings

[0019] Figure 1 Flow chart of an iterative power reactor neutron noise analysis method based on the Monte Carlo method of the present invention.

[0020] Figures 2 to 5 Schematic diagram of the calculation results of the implementation case of the present invention, showing the phase and amplitude of the fast group and thermal group neutron noise corresponding to the frequency ω = 1 Hz.

[0021] Figure 2 Graph of the calculation results of the fast group neutron noise amplitude.

[0022] Figure 3 Graph of the calculation results of the thermal group neutron noise amplitude.

[0023] Figure 4 Graph of the calculation results of the fast group neutron noise phase.

[0024] Figure 5 Graph of the calculation results of the thermal group neutron noise phase. Detailed implementation method

[0025] The present invention will be further described in detail below through specific implementation methods.

[0026] As Figure 1 shown, an iterative power reactor neutron noise analysis method based on the Monte Carlo method of the present invention is implemented by adopting the following technical solutions:

[0027] Step 1. Use the Monte Carlo program to accurately model the spatial geometry and material composition of the target power reactor core, and define the spatial position, perturbation cross-section (perturbed total cross-section, perturbed scattering cross-section, perturbed fission neutron production cross-section) and phase of the perturbed material source at the calculation frequency points, and fill in the program input cards;

[0028] Step 2. Use the critical calculation mode of Monte Carlo to set the statistical active generations. After reaching the statistical active generations, calculate the neutron noise source term at the calculation frequency points according to formula (1); this neutron noise source term will be used as the input for the next neutron noise transport calculation;

[0029]

[0030] In the formula: S(r,Ω,E,ω) — represents the neutron noise source term corresponding to neutrons at position r, in the direction of Ω, with energy E and perturbation frequency ω

[0031] δΣ t (r,E,ω) — represents the perturbed total cross-section corresponding to neutrons at position r, with energy E and perturbation frequency ω

[0032] Ψ0(r,Ω,E) — represents the steady-state neutron flux density of neutrons at position r, in the direction of Ω, with energy E δΣs (r, Ω'→Ω, E'→E, ω) —— represents the perturbed scattering cross section corresponding to neutrons scattered from direction Ω' to Ω, with energy scattered from E' to E at position r, when the perturbation frequency is ω

[0033] υδΣ f (r, E', ω) —— represents the perturbed fission neutron production cross section corresponding to neutrons with energy E' at position r, when the perturbation frequency is ω

[0034] χ p (E) —— represents the prompt fission neutron spectrum of neutrons with energy E

[0035] —— represents the delayed fission neutron spectrum of neutrons with energy E, where i d represents the delayed neutron group

[0036] k eff —— a constant representing the effective multiplication factor

[0037] —— a constant representing the decay constant of the precursor nuclei of the i d th group of delayed neutrons

[0038] β —— a constant representing the delayed neutron fraction, which is the sum of the delayed neutron fractions of the i d th group of delayed neutrons

[0039] Step 3. Reconstruct and transform the traditional neutron noise equation to construct an iterative format for the Monte Carlo method; the traditional neutron noise equation is in the form shown in formula (2)

[0040]

[0041] In the formula: δΨ(r, Ω, E, ω) —— represents the perturbed neutron flux density corresponding to neutrons with energy E in the direction Ω at position r, when the perturbation frequency is ω, that is, the neutron noise flux

[0042] Σ t (r, E) —— represents the total cross section corresponding to neutrons with energy E at position r

[0043] η —— a real parameter, generally taken as 1 in neutron noise calculations

[0044] v(r, E) —— represents the velocity of neutrons with energy E at position r

[0045] i —— the imaginary unit

[0046] Σ s(r, Ω' → Ω, E' → E) —— represents the scattering cross section corresponding to neutrons that are scattered from direction Ω' to direction Ω and whose energy is scattered from E' to E at position r

[0047] υΣ f (r, E') —— represents the fission neutron production cross section at position r with energy E'

[0048] k eff —— a constant representing the effective multiplication factor

[0049] The process of constructing the iterative format is as follows:

[0050] First, the original equation (2) can be written in the following operator form (3):

[0051] Ψ = (L - P - D - Ps) -1 S (3)

[0052] Ψ is the neutron noise flux, L is the transport operator, P is the prompt fission operator, D is the delayed fission operator, Ps is the pseudo fission operator, and S is the neutron noise source term

[0053] Then, the scaling factor k is defined s :

[0054]

[0055] where the angled brackets <> represent integration over the phase space.

[0056] According to the definition of the scaling factor k s Equation (3) is rewritten in the following equivalent form:

[0057]

[0058] Based on equations (4) and (5), an iterative format is constructed to obtain equations (6) and (7):

[0059]

[0060] The subscripts n and n - 1 in equations (6) and (7) represent the number of iterations.

[0061] Step 4. Set the maximum number of iterations to n times, count the number of active generations as h generations, based on the neutron noise source term calculated in Step 2, sample the initial noise source particle distribution as the starting point for the first - generation iteration, and enter the Monte Carlo iterative calculation according to equations (6) and (7). During the iterative calculation process, according to equation (7), the generated prompt fission neutrons are stored in the fission library, and the delayed fission neutrons are directly simulated using the method of secondary particles.

[0062] Step 5. Perform iterative calculations, and continuously update the scaling factor k according to formulas (6) and (7). s,n and the distribution of noise source particles. The scaling factor k s,n is calculated by formula (6); when updating the distribution of noise source particles, it is necessary to discuss according to k s,n in different cases: Generally speaking, k s,n < 1, then in the distribution of noise source particles, the proportion of particles from the neutron noise source term S is 1 - k s,n , and the proportion of particles from the fission library particles stored in step 4 is k s,n ; if k s,n ≥ 1, then directly set k s,n to 1, indicating that there are no particles from the neutron noise source term S, and all particles in the noise source particle distribution come from the fission library stored in step 4.

[0063] Step 6. When the calculation reaches the set maximum number of iterations n times, enter the h-generation statistical active generation, perform statistical averaging on the h-generation statistical active generation, and obtain the average scaling factor k s,avg and the spatial distribution of neutron noise Ψ avg . Then perform result normalization. Since the scaling factor k s for the external source term is introduced, it is necessary to scale the calculation result Ψ avg according to formula (8) to obtain the final result, that is, the actual spatial distribution of neutron noise Ψ actual :

[0064]

[0065] According to formula (8), the spatial distribution of neutron noise Ψ actual corresponding to the calculated frequency point can be calculated. Finally, output the final result.

[0066] Taking the simplified C5G7 neutron noise benchmark problem as an example, applying the method of the present invention to calculate the spatial distribution of neutron noise at the 3*3 fuel rod centered on the perturbation region with a frequency ω = 1 Hz, the results are as Figures 2 to 5 shown. As Figure 2 shown is the calculation result graph of the fast-group neutron noise amplitude. It can be seen from the figure that the fast-group neutron flux amplitude in the perturbed fuel rod is relatively large, and the fast neutron flux amplitude in the nearby space is also affected to a certain extent. As Figure 3 shown is the calculation result graph of the thermal-group neutron noise amplitude. It can be seen from the figure that the thermal-group neutron flux amplitude in the perturbed fuel rod and its adjacent water hole is relatively large, and the thermal neutron flux amplitude in the nearby space is also affected to a certain extent. As Figure 4 shown is the calculation result graph of the fast-group neutron noise phase. It can be seen from the figure that the fast-group neutron noise phase near the perturbation source is relatively prominent. As Figure 5The figure shows the calculation results of the thermal group neutron noise phase. It can be seen from the figure that the thermal group neutron noise phase near the perturbation source is relatively prominent.

Claims

1. An iterative dynamic reactor neutron noise analysis method based on the Monte Carlo method, characterized in that, The method includes the following specific steps: Step 1. Accurately model and describe the spatial geometric composition and material components of the core of the target power reactor, and accurately model and describe the spatial position, perturbation cross-section and phase of the perturbation material source at the calculation frequency points; Step 2. Use the critical calculation mode of the Monte Carlo method, set the statistical active generations, and after reaching the statistical active generations, calculate the neutron noise source term at the calculation frequency points; Step 3. Reconstruct and transform the traditional neutron noise equation to construct the iterative format of the Monte Carlo method; Step 4. According to the neutron noise source term calculated in Step 2, sample the initial noise source particle distribution, and start the Monte Carlo iterative loop calculation according to the iterative format; Step 5. In the core of the target power reactor, perform neutron noise transport calculations, store the generated prompt fission neutrons in the fission bank, and simulate the delayed fission neutrons using secondary particles; after all the particles of this generation are simulated, update the scaling factor k according to the number of particles in the fission bank s,n and the particle distribution of the noise source, and construct a new generation of source distribution based on the fission bank and the noise source term; Step 6. When the set maximum number of iterations is reached, enter the statistical active generation, perform statistical averaging and result normalization on the statistical active generation, and obtain the average scaling factor k s,avg and the spatial distribution characteristics of neutron noise.

2. The iterative dynamic reactor neutron noise analysis method based on the Monte Carlo method according to claim 1, characterized in that The perturbation cross-section in Step 1 includes the perturbed total cross-section, the perturbed scattering cross-section and the perturbed fission neutron production cross-section.

3. An iterative dynamic reactor neutron noise analysis method based on the Monte Carlo method according to claim 1, characterized in that In Step 2, the neutron noise source term at the calculation frequency points is calculated according to formula (1); In the formula: S(r,Ω,E,ω) — represents the neutron noise source term corresponding to neutrons at position r, in the direction of Ω, with energy E and perturbation frequency ω δΣ t (r, E, ω) —— represents the total perturbation cross section corresponding to neutrons with energy E at position r and perturbation frequency ω Ψ0(r,Ω,E) — represents the steady-state neutron flux density of neutrons at position r, in the direction of Ω, with energy E δΣ s (r, Ω'→Ω, E'→E, ω)——represents the differential scattering cross section corresponding to neutrons scattered from the direction Ω' to the direction Ω, with energy scattered from E' to E, at the position r and with a perturbation frequency of ω υδΣ f (r, E', ω) —— represents the corresponding perturbation fission neutron production cross-section at position r for neutrons with energy E' and perturbation frequency ω χ p (E)——represents the prompt fission neutron spectrum of neutrons with energy E —— represents the delayed fission neutron spectrum of neutrons with energy E, where i d represents the delayed neutron group k eff —— A constant representing the effective multiplication factor —— A constant, representing the d decay constant of the delayed neutron precursor nuclei in the i-th group β—— a constant representing the delayed neutron fraction, which is the sum of the delayed neutron fractions of the i d th group 4. An iterative dynamic reactor neutron noise analysis method based on the Monte Carlo method according to claim 1, characterized in that In Step 3, the form of the traditional neutron noise equation is as shown in formula (2); In the formula: δΨ(r,Ω,E,ω) — represents the perturbed neutron flux density corresponding to neutrons at position r, in the direction of Ω, with energy E and perturbation frequency ω, that is, the neutron noise flux Σ t (r,E) —— represents the total cross section corresponding to neutrons with energy E at position r η — real number parameter v(r,E) — represents the neutron velocity at position r with energy E i — imaginary unit Σ s (r, Ω' → Ω, E' → E) —— represents the scattering cross section corresponding to neutrons that are scattered from the direction Ω' to the direction Ω and have their energy scattered from E' to E at the position r υΣ f (r, E') —— represents the fission neutron production cross section at position r with energy E' k eff —— A constant representing the effective multiplication factor The process of constructing the iterative format is as follows: First, the original equation (2) can be written in the following operator form (3): Ψ = (L - P - D - Ps) -1 S (3) Ψ is the neutron noise flux, L is the transport operator, P is the prompt fission operator, D is the delayed fission operator, Ps is the pseudo-fission operator, and S is the neutron noise source term Then define the scaling factor k s as follows: Among them, the angular brackets <> represent integration over the phase space; According to the definition of the scaling factor k s Formula (3) is rewritten into the following equivalent form: Construct the iterative format according to formula (4) and formula (5) to obtain formula (6) and formula (7); The subscripts n and n-1 in formula (6) and formula (7) represent the number of iterations.

5. An iterative dynamic reactor neutron noise analysis method based on the Monte Carlo method according to claim 1, characterized in that In step 8, the obtained spatial distribution of neutron noise is scaled by an average scaling factor to obtain the spatial distribution Ψ of neutron noise corresponding to the frequency point actual , and the formula is as follows: where: Ψ avg —— represents the neutron noise spatial distribution k obtained in step 7 s,avg —— represents the average scaling factor.

Images