A fast simulation method of reactor neutron noise based on Green's function

Abstract

A Green's function-based rapid simulation method for reactor neutron noise comprises the following steps: according to the basic parameters of the reactor, a steady-state effective multiplication factor and a steady-state neutron flux density are obtained through a steady-state neutron transport equation; unit point source parameters are initialized and set; the Green's function form of the frequency-domain neutron noise equation is cyclically solved in combination with the obtained steady-state effective multiplication factor and steady-state neutron flux density; the distribution of the frequency-domain neutron noise Green's function with respect to energy group, spatial variable, angular variable, and frequency variable excited by each unit point source is obtained, and a frequency-domain neutron noise Green's function database is generated; then, according to the neutron noise spectrum excited by an arbitrary noise source, a linear superposition of the Green's function and the noise source term is used for rapid calculation. The present invention simplifies the solution of the neutron noise spectrum under arbitrary noise sources into a linear superposition calculation, thereby improving the computational efficiency of numerical simulation of reactor neutron noise.

Description

Technical Field

[0001] The present invention relates to a technology in the field of reactor control, in particular to a method for rapid simulation of reactor neutron noise based on Green's function. Background Art

[0002] During steady-state operation of a nuclear reactor, the reactor's neutron flux density does not ideally remain constant. Instead, it fluctuates randomly around its steady-state value. This random fluctuation is known as reactor neutron noise. Neutron noise can cause deviations from normal reactor operation, adversely affecting the economics and safety of reactor operations. The effects of neutron noise on reactor operation can be simulated by solving the frequency-domain neutron noise equation. Summary of the Invention

[0003] The present invention addresses the problem that the existing calculation method for the theoretical spectrum of neutron noise is based on neutron diffusion theory and has insufficient calculation accuracy when dealing with cores with complex geometric configurations. A rapid simulation method for reactor neutron noise based on Green's function is proposed. By calculating the neutron noise spectrum response under a set of unit point sources, a reactor neutron noise Green's function database is created based on transport theory. This simplifies the solution of the neutron noise spectrum under any noise source to a linear superposition calculation, thereby improving the computational efficiency of the numerical simulation of reactor neutron noise.

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

[0005] The present invention relates to a method for rapid simulation of reactor neutron noise based on Green's function, comprising:

[0006] Step 1: According to the basic parameters of the reactor, the steady-state effective multiplication factor and the steady-state neutron flux density are obtained through the steady-state neutron transport equation;

[0007] Step 2: Initialize the unit point source parameters and set the unit point source. Combined with the steady-state effective multiplication factor and steady-state neutron flux density obtained in step 1, the Green's function form of the frequency domain neutron noise equation is solved cyclically to obtain the distribution of the frequency domain neutron noise Green's function of each unit point source excitation with respect to energy group, spatial variable, angle variable and frequency variable.

[0008] G gs→g (r s →r,Ω s →Ω,ω s →ω) and generate a frequency domain neutron noise Green's function database;

[0009] In the loop solution, the angle variables and the space variables are obtained by using numerical discrete methods, including but not limited to the spherical harmonic function method (P N ), simplified spherical harmonics method (SPN ), finite difference method, finite element method, etc.

[0010] Step 3: Based on the neutron noise spectrum under the excitation of any noise source, the Green's function is quickly calculated by linear superposition of the noise source term.

[0011] The present invention relates to a reactor neutron noise rapid simulation system for realizing the above-mentioned method, comprising: a parameter reading and preprocessing module, a steady-state problem solving module, a noise problem solving module, a noise source setting module, a Green's function solving module and a Green's function storage module, wherein: the parameter reading and preprocessing module reads the reactor parameters input by the user and performs preprocessing; the steady-state problem solving module solves the steady-state neutron transport equation according to the reactor core parameters to obtain the steady-state effective proliferation factor and the steady-state neutron flux density distribution; the noise problem solving module calls the noise source setting module according to the reactor core parameters and the calculation setting parameters module and Green's function solving module, and controls the execution of related modules; the noise source setting module sets the noise source term to an appropriate unit point source form according to the reactor core parameters and the calculation setting parameters; the Green's function solving module solves the Green's function form of the frequency domain neutron noise equation according to the reactor core parameters and the calculation results of the steady-state problem solving module, obtains the Green's function under the current unit point source, and passes it to the Green's function storage module; the Green's function storage module converts the current calculation parameters and the calculation results of the Green's function solving module into an appropriate data structure, and stores it in a computer-readable and writable medium.

[0012] Technical Effects

[0013] Based on neutron transport theory and the Green's function method, the present invention transforms the problem of simulating complex reactor neutron noise into the problem of solving the Green's function form of a set of frequency-domain neutron noise equations, and provides a specific expression of the Green's function form of the frequency-domain neutron noise equations. Compared with the existing technology, which can only handle reactor systems with known geometric curvature, and the calculation of geometric curvature usually relies on the assumption of a uniform medium, it lacks the processing capability for reactors with complex geometry and material distribution. To address this problem, the present invention improves the frequency-domain neutron noise equation and its Green's function form, making it no longer dependent on the assumption of a uniform medium. Only the core geometry, material layout, and neutronic properties of the materials need to be known to solve the Green's function, thus solving the problem of multiple assumptions and difficult solution of reactor geometric curvature. On the other hand, the existing technical solutions are derived based on neutron diffusion theory, and many assumptions are introduced for the angle variable, making it difficult to handle the numerical simulation of neutron noise in strongly absorbing and strongly anisotropic media. Compared with the existing technical solutions, the present invention adopts neutron transport theory, which can process angle variables more accurately, solves the defect that the existing technical solutions can only process weakly absorbing and weakly anisotropic media, and has the ability to simulate neutron noise in complex reactor systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Flowchart of the present invention;

[0015] Figure 2 Schematic diagram of the system of the present invention;

[0016] Figure 3 Schematic diagram of the geometry and material arrangement of the embodiment;

[0017] Figure 4 The calculation results are applied for the example. DETAILED DESCRIPTION

[0018] like Figure 1 As shown, this embodiment relates to a method for rapid simulation of reactor neutron noise based on Green's function, comprising:

[0019] Step 1: According to the basic parameters of the reactor, the steady-state effective multiplication factor and steady-state neutron flux density are obtained through the steady-state neutron transport equation.

[0020] The steady-state neutron transport equation is specifically: Where: k eff,0 is the steady-state effective proliferation factor, ψ g,0 (r,Ω) is the distribution of the steady-state neutron flux density of the gth group with respect to spatial and angular variables, ψ g',0 (r,Ω') Similarly, r is a spatial variable, Ω and Ω' are angle variables, is the differential operator, ω is the frequency variable, g and g' are the energy group numbers, Σ t,g,0 (r) is the distribution of the total steady-state neutron cross section of the g-th group with respect to spatial variables, Σ s,g′→g,0 (r,Ω'→Ω) is the distribution of the steady-state neutron scattering cross section from the g'th group to the g'th group and from the Ω' angle to the Ω angle with respect to spatial variables and angular variables, ν is the average number of neutrons produced per fission, Σ f,g′,0 (r) is the distribution of the steady-state neutron fission cross section of the g'th group with respect to spatial variables, and the distribution of the steady-state neutron energy spectrum of the g'th group with respect to spatial variables r is a spatial variable, g is the energy group number, q is the group number of the delayed neutron precursor nucleus, χ p,g (r) is the distribution of prompt neutron energy spectrum of group g with respect to spatial variables, β q (r) is the distribution of the delayed neutron fraction of the qth group with respect to spatial variables, χ d,q,g (r) is the distribution of delayed neutron energy spectrum from group q to group g with respect to spatial variables.

[0021] Step 2: Initialize the unit point source parameters and set the unit point source. Combined with the steady-state effective multiplication factor and steady-state neutron flux density obtained in step 1, the Green's function form of the frequency domain neutron noise equation is solved cyclically to obtain the distribution of the frequency domain neutron noise Green's function of each unit point source excitation with respect to energy group, spatial variable, angle variable and frequency variable. And generate the frequency domain neutron noise Green's function database, specifically:

[0022] Among them: Ω and Ω' are angle variables, is the differential operator, r is the spatial variable, ω is the frequency variable, and the unit point source parameters include the energy group g s , spatial variable r s , angle variable Ω s and frequency variable ω s , g and g' are energy group numbers, is the distribution of the g-th group neutron noise Green's function with respect to spatial variables, angle variables and frequency variables, Similarly, Σ s,g′→g,0 (r,Ω'→Ω) is the distribution of the steady-state neutron scattering cross section from the g'th group to the g'th group and from the Ω' angle to the Ω angle with respect to spatial variables and angular variables, ν is the average number of neutrons produced per fission, Σ f,g′,0 (r) is the distribution of the steady-state neutron fission cross section of the g'th group with respect to spatial variables, is the distribution of the total dynamic neutron cross section of the gth group with respect to spatial variables and frequency variables, is the distribution of the dynamic neutron energy spectrum of the gth group with respect to spatial variables and frequency variables, For the g s Group, spatial position is r s , angle is Ω s , frequency is ω s The distribution of the unit point source with respect to energy group, spatial variable, angle variable and frequency variable, k eff,0 It is a steady-state effective growth factor.

[0023] Step 3: Based on the neutron noise spectrum under the excitation of any noise source, a fast calculation is performed by linear superposition of the Green's function and the noise source term, specifically:

[0024] Among them: r is the spatial variable, r s is the spatial variable of the noise source term, Ω is the angle variable, s is the angle variable of the noise source term, ω is the frequency variable, ω s is the frequency variable of the noise source term, g is the energy group number, g s is the energy group number of the noise source term, δψ g(r,Ω,ω) is the distribution of the neutron noise spectrum of the g-th group with respect to spatial variables, angle variables and frequency variables,

[0025] is the distribution of the g-th group neutron noise spectrum with respect to spatial variables, angle variables and frequency variables, For the g s Group, spatial position is r s , angle is Ω s , frequency is ω s The noise source term.

[0026] After specific practical experiments, Figure 3 For example, the C4V benchmark problem shown in the figure is composed of two UO2 modules and two MOX modules arranged in an alternating pattern, each of which contains 17×17 uniform grid cells, and the side length of each grid cell is 1.26 cm. Figure 3 As shown, the UO2 assembly includes 25 guide tube grid cells and 264 UO2 grid cells, and the MOX assembly includes 25 guide tube grid cells, 100 internal MOX fuel grid cells, 100 middle MOX fuel grid cells and 64 external MOX fuel grid cells. Among the four boundaries, the left boundary and the upper boundary are set as reflection boundary conditions, and the right boundary and the lower boundary are set as vacuum boundary conditions. The results obtained after the rapid simulation of reactor neutron noise by the present invention are as follows: Figure 4 As shown, it shows that it has the ability to calculate and analyze neutron noise in the frequency domain at the gate element level.

[0027] Compared with the existing technology, this method is based on neutron transport theory and has the ability to carry out gate element scale simulation of reactor core neutron noise. Compared with the component scale simulation based on neutron diffusion theory in the existing technology, it can obtain higher resolution neutron noise spectrum.

[0028] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principles and purpose of the present invention. The scope of protection of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. All implementation schemes within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for rapid simulation of reactor neutron noise based on Green's function, characterized in that: include: Step 1: According to the basic parameters of the reactor, the steady-state effective multiplication factor and the steady-state neutron flux density are obtained through the steady-state neutron transport equation; Step 2: Initialize the unit point source parameters and set the unit point source. Combined with the steady-state effective multiplication factor and steady-state neutron flux density obtained in step 1, the Green's function form of the frequency domain neutron noise equation is solved cyclically to obtain the distribution of the frequency domain neutron noise Green's function of each unit point source excitation with respect to energy group, spatial variable, angle variable and frequency variable. And generate a frequency domain neutron noise Green's function database, where: is a spatial variable, is the spatial variable of the noise source term, is the angle variable, is the angular variable of the noise source term, is the frequency variable, is the frequency variable of the noise source term; Step 3: Based on the neutron noise spectrum under the excitation of any noise source, a fast calculation is performed by linear superposition of the Green's function and the noise source term; The linear superposition fast calculation is specifically as follows: ,in: is the energy group number, is the energy group number of the noise source term, For the The distribution of the neutron noise spectrum of the group with respect to spatial variables, angle variables and frequency variables, For the The distribution of the neutron noise spectrum of the group with respect to spatial variables, angle variables and frequency variables, For the Group, spatial position is , angle is , the frequency is The noise source term.

2. The method for rapid simulation of reactor neutron noise based on Green's function according to claim 1, characterized in that: The steady-state neutron transport equation is specifically: ,in: It is a steady-state effective growth factor. For the The distribution of the group steady-state neutron flux density with respect to spatial and angular variables, For the The distribution of the group steady-state neutron flux density with respect to spatial and angular variables, is a spatial variable, and is the angle variable, is the differential operator, is the frequency variable, and is the energy group number, For the The distribution of the group's steady-state total neutron cross section with respect to spatial variables, For the Group to Group, from Angle to The distribution of the steady-state neutron scattering cross section with respect to spatial and angular variables, is the average number of neutrons produced per fission, For the The distribution of the steady-state neutron fission cross section of the group with respect to spatial variables, Distribution of the Steady-State Neutron Energy Spectrum of a Group with Respect to Spatial Variables , is a spatial variable, is the energy group number, is the group number of the delayed neutron precursor nucleus, For the The distribution of the prompt neutron energy spectrum of the group with respect to spatial variables, For the The distribution of the delayed neutron fraction of the group with respect to spatial variables, For the Group to The distribution of the delayed neutron energy spectrum of the group with respect to spatial variables.

3. The method for rapid simulation of reactor neutron noise based on Green's function according to claim 1, characterized in that: The Green function form of the frequency domain neutron noise equation is specifically: ,in: and is the angle variable, is the differential operator, is a spatial variable, is a frequency variable, and the unit point source parameters include energy groups , spatial variables , angle variables and frequency variables , and is the energy group number, For the The distribution of the Green's function of group neutron noise with respect to spatial variables, angle variables and frequency variables, No. The distribution of the Green's function of group neutron noise with respect to spatial variables, angle variables and frequency variables, For the Group to Group, from Angle to The distribution of the steady-state neutron scattering cross section with respect to spatial and angular variables, is the average number of neutrons produced per fission, For the The distribution of the steady-state neutron fission cross section of the group with respect to spatial variables, For the The distribution of the group's dynamic total neutron cross section with respect to spatial and frequency variables, For the The distribution of the dynamic neutron energy spectrum of the group with respect to spatial variables and frequency variables, For the Group, spatial position is , angle is , the frequency is The distribution of the unit point source with respect to energy group, spatial variable, angle variable and frequency variable, It is a steady-state effective growth factor.

4. A reactor neutron noise fast simulation system based on Green's function for implementing the method according to any one of claims 1 to 3, characterized in that: include: Parameter reading and preprocessing module, steady-state problem solving module, noise problem solving module, noise source setting module, Green's function solving module and Green's function storage module, wherein: the parameter reading and preprocessing module reads the reactor parameters input by the user and performs preprocessing; the steady-state problem solving module solves the steady-state neutron transport equation according to the reactor core parameters to obtain the steady-state effective proliferation factor and the steady-state neutron flux density distribution; the noise problem solving module calls the noise source setting module and the Green's function solving module according to the reactor core parameters and the calculation setting parameters, and controls the execution of related modules; the noise source setting module sets the noise source term to an appropriate unit point source form according to the reactor core parameters and the calculation setting parameters; the Green's function solving module solves the Green's function form of the frequency domain neutron noise equation according to the reactor core parameters and the calculation results of the steady-state problem solving module, obtains the Green's function under the action of the current unit point source, and passes it to the Green's function storage module; The Green's function storage module converts the current calculation parameters and the calculation results of the Green's function solution module into an appropriate data structure and stores it in a computer-readable and writable medium.

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