Rapid reactor neutron noise simulation method based on Green function

Abstract

The invention discloses a reactor neutron noise rapid simulation method based on a Green function, and the method comprises the steps: obtaining a steady-state effective multiplication factor and a steady-state neutron flux density through a steady-state neutron transport equation according to basic parameters of a reactor; initializing a unit point source parameter and setting a unit point source, and circularly solving a Green function form of a frequency domain neutron noise equation by combining the obtained steady-state effective multiplication factor and steady-state neutron-flux density; obtaining the distribution of the frequency-domain neutron noise Green function excited by each unit point source about an energy group, a space variable, an angle variable and a frequency variable, and generating a frequency-domain neutron noise Green function database; and according to a neutron noise spectrum under excitation of any noise source, rapid calculation is carried out through linear superposition of a Green function and a noise source item. According to the method, the solution of the neutron noise spectrum under any noise source is simplified into linear superposition calculation, and the calculation efficiency of reactor neutron noise numerical simulation is improved.

Description

Technical Field

[0001] The 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] In the actual process of steady-state operation of nuclear reactors, the neutron flux density of the reactor does not ideally maintain a constant value, but is in a state of random fluctuations around the steady-state value. This random fluctuation is called the neutron noise of the reactor. The neutron noise phenomenon causes the operating state of the reactor to deviate from the normal state, which has an adverse effect on the economy and safety of the reactor operation. The effect of neutron noise on the operating state of the reactor can be simulated by solving the frequency domain neutron noise equation. Summary of the invention

[0003] The present invention aims at the problem that the existing calculation method of the theoretical spectrum of neutron noise is based on the neutron diffusion theory and has insufficient calculation accuracy when dealing with a core with complex geometric configuration. A rapid simulation method of reactor neutron noise based on Green's function is proposed. By calculating the neutron noise spectrum response under a group of unit point sources excitation, a reactor neutron noise Green's function database is prepared based on transport theory, so that the solution of the neutron noise spectrum under any noise source is simplified to linear superposition calculation, thereby improving the calculation 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 proliferation 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. G gs→g (r s →r,Ω s →Ω,ω s →ω) and generate a frequency domain neutron noise Green's function database;

[0008] In the loop solution, the angle variables and the space variables are obtained by numerical discretization methods, including but not limited to the spherical harmonic function method (P N ), simplified spherical harmonics method (SP N), finite difference method, finite element method, etc.

[0009] Step 3: According to 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.

[0010] The present invention relates to a reactor neutron noise rapid simulation system for realizing the above 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. Technical Effects

[0011] Based on neutron transport theory and Green's function method, the present invention transforms the complex reactor neutron noise simulation problem into the problem of solving a set of frequency domain neutron noise equations in Green's function form, and gives a specific expression of the frequency domain neutron noise equation in Green's function form. Compared with the prior art, which can only handle reactor systems with known geometric curvature, and the calculation of geometric curvature usually relies on the assumption of uniform medium, but lacks processing capabilities for reactors with complex geometry and material distribution. In view of this problem, the present invention improves the frequency domain neutron noise equation and its Green's function form, so that it no longer relies on the assumption of uniform medium. Only the core geometry, material layout and neutronic properties of the material need to be known to solve the Green's function, solving the problem of many assumptions and difficult calculation of reactor geometric curvature. On the other hand, the prior art solution is derived based on neutron diffusion theory, and many assumptions are introduced for angle variables, making it difficult to handle the neutron noise numerical simulation problem of strong absorption and strong 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 weak absorption and weak anisotropic media, and has the ability to simulate neutron noise in complex reactor systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a flow chart of the present invention;

[0013] Figure 2 It is a schematic diagram of the system of the present invention;

[0014] Figure 3 Schematic diagram of geometry and material arrangement of the embodiment;

[0015] Figure 4 The calculation results are applied for the example. DETAILED DESCRIPTION

[0016] like Figure 1 As shown, this embodiment relates to a method for rapid simulation of reactor neutron noise based on Green's function, comprising:

[0017] 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.

[0018] 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 variables 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 steady-state neutron cross section of the g-th group with respect to the spatial variable, 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 the spatial variable, and the distribution of the steady-state neutron energy spectrum of the gth group with respect to the spatial variable 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 the spatial variable, χ d,q,g (r) is the distribution of delayed neutron energy spectrum from the qth group to the gth group with respect to spatial variables.

[0019] Step 2: Initialize the unit point source parameters and set the unit point source. Combined with the steady-state effective proliferation 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:

[0020] 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 g-th 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 proliferation factor.

[0021] Step 3: According to 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, specifically: Among them: r is the spatial variable, r s is the spatial variable of the noise source term, Ω is the angle variable, Ω 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 noise spectrum of the g-th group neutrons with respect to spatial variables, angle variables and frequency variables, is the distribution of the noise spectrum of the g-th group neutrons 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.

[0022] After specific practical experiments, Figure 3 As an example, the C4V benchmark question shown in the figure consists of two UO 2 The modules and 2 MOX modules are arranged alternately, each module contains 17×17 homogenization grid cells, and the side length of each grid cell is 1.26 cm. Figure 3 As shown, the UO 2 The 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 reactor neutron noise fast simulation 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.

[0023] Compared with the existing technology, this method is based on neutron transport theory and has the ability to carry out gate element scale reactor core neutron noise simulation. Compared with the component scale simulation based on neutron diffusion theory in the existing technology, it can obtain a higher resolution neutron noise spectrum.

[0024] 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 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 proliferation 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 frequency domain neutron noise Green's function database; Step 3: According to 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.

2. The method for rapid simulation of reactor neutron noise based on Green's function according to claim 1 is characterized in that: 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 variables and angular variables, ψ g',0 (r,Ω') Similarly, r is the 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 steady-state neutron cross section of the g-th group with respect to the spatial variable, 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 the spatial variable, and the distribution of the steady-state neutron energy spectrum of the gth group with respect to the spatial variable 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 the spatial variable, χ d,q,g (r) is the distribution of delayed neutron energy spectrum from the qth group to the gth 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: Among them: Ω and Ω' are angle variables, ▽ is the differential operator, r is the space 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 g-th 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 proliferation factor.

4. The method for rapid simulation of reactor neutron noise based on Green's function according to claim 1, characterized in that: The linear superposition fast calculation is specifically as follows: Among them: r is the spatial variable, r s is the spatial variable of the noise source term, Ω is the angle variable, Ω 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 noise spectrum of the g-th group neutrons with respect to spatial variables, angle variables and frequency variables, is the distribution of the noise spectrum of the g-th group neutrons 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.

5. A reactor neutron noise fast simulation system based on Green's function for implementing any of the methods described in claims 1-4, 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 calculation results of the reactor core parameters and 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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