CN111584019B - A Method of Obtaining the Response of Detectors Outside the Reactor Based on First Collision Source-Monte Carlo Coupling - Google Patents

Abstract

Method for obtaining response of detector outside reactor based on first collision source-Monte Carlo coupling, according to material and geometry of reactorThe method is characterized in that a reactor region is divided into an in-core region containing a reactor core, a reflecting layer and a shielding layer and an out-of-core region containing an out-of-core detector, and the neutron flux density at the out-of-core detector is divided into non-collision neutron flux density phi according to a primary collision source technology ^u (r, E) and collision neutron flux density phi ^c (r, E); calculating non-collision neutron flux density phi from external neutron point source by using semi-analytic ray tracing method ^u (r, E) with primary collision source Q ^c (r, Ω, E); from the first collision source Q using the Monte Carlo method ^c (r, omega, E) calculating to obtain collision neutron flux density phi ^c (r, E); adding the two parts of neutron flux densities at the position of the out-of-pile detector to obtain the neutron flux density at the position of the out-of-pile detector, and calculating the detector response according to the neutron flux density at the position of the out-of-pile detector; in the method, based on the first collision source technology, the advantages of the Monte Carlo method and the semi-analytic ray tracing method are respectively utilized, and the statistical efficiency and the calculation accuracy of the deep penetration problem are improved.

Description

Obtaining the Response of Detectors Outside the Reactor Based on the First Collision Source-Monte Carlo Coupling method

technical field

The invention relates to calculation of nuclear reactor core deep penetration problem, in particular to a method for obtaining the response of a detector outside the reactor based on the first collision source-Monte Carlo coupling.

Background technique

The Monte Carlo method is also called the probability theory method. This method first establishes a model so that the solution of the problem is the mathematical expectation of a random variable, or a quantity related to the mathematical expectation, and then statistically estimates the random variable's The arithmetic mean of several specific observations is the solution to the problem. Use the Monte Carlo method to solve the neutron transport equation, build a model based on the physical process of neutron transport, simulate the movement history of a large number of neutrons, and count their contributions to the neutron flux density or other responses to obtain Statistical estimates of neutron flux density or other responsive quantities.

Use the Monte Carlo method to simulate directly from the external neutron point source, that is, use the Monte Carlo method to simulate the whole process, which has the problems of large amount of calculation and low statistical efficiency of the target detector; The flight direction of the neutrons is biased, the neutrons with a large deviation from the target direction are discarded, and the weight of the remaining neutrons is increased. While ensuring unbiasedness, the number of simulations in the target area is increased to reduce the variance and the total amount of simulation calculations. Using source bias to start the simulation from a single point source, only the direction of the point source is biased. During the simulation process of the remaining neutrons, some neutrons collide and fly away from the direction of the target detector gradually. The statistical contribution of the neutron flux density is very small, and the Monte Carlo method will increase the amount of calculation to track this part of neutrons; from the definition of the quality factor, it can be known that the quality factor is inversely proportional to the product of the calculation time and the square of the statistical relative error, when When the statistical relative error is guaranteed to be constant, the longer the calculation time and the lower the quality factor, the lower the statistical efficiency of the target position.

Contents of the invention

The purpose of the present invention is to provide a method based on the first collision source-Monte Carlo coupling to obtain the response of the detector outside the reactor. Coupling the Carlo method, making full use of the advantages of fast calculation in the deep penetration problem of the deterministic method and the advantages of the Monte Carlo method in dealing with the complex geometric problems of the extra-core detector in the deep penetration problem, combined with the first collision source technology to generate the first In the Monte Carlo calculation part of the collision source optimization shielding calculation, the external neutron source distributed only in the reactor area is converted into the first collision source distributed in the entire reactor area, compared with the Monte Carlo method directly starting from the external neutron source According to calculations, the number of particles arriving at the detector outside the pile is more, and the biased sampling operation can be performed on the spatial distribution of the first collision source to further increase the number of particles arriving at the detector outside the pile, which can increase the neutron flux at the detector outside the pile. The calculation efficiency of the flux density makes the calculation of the neutron flux density at the target detector more accurate and fast;

In order to achieve the above object, the present invention has taken the following technical solutions to implement:

A method for obtaining the response of a detector outside the reactor based on the first collision source-Monte Carlo coupling, the method includes the following steps:

Step 1: According to the material and geometric characteristics of the reactor, the reactor area is divided into the inner area including the core, reflector and shielding layer, and the outer area including the outer detector. According to the neutron flux density of the first collision source technology Divided into the uncollided neutron flux density φ ^u (r, E) and the collided neutron flux density φ ^c (r, E); the whole reactor area is divided into a three-dimensional rectangular coordinate grid, and the actual neutron sources inside and outside the reactor are volume source, transforming the external neutron volume source into an external neutron point source located at the center of the grid in the source area, the conversion method is: the intensity distribution of the external neutron volume source is integrated with the volume of the grid where it is located, and the point source located at the grid is obtained The neutron point source at the center is strong, that is, the body source in the entire grid is equivalent to the point source at the center of the grid; starting from the outer neutron point source, the non-collision of the entire reactor area is calculated by semi-analytical ray tracing method Flux density φ ^u (r,E); for an external neutron point source, the angular flux of uncollided neutrons at a specified position r in the arrival space generated from the neutron point source r _p is calculated using the semi-analytic ray tracing method Density φ ^u (r, Ω, E), the calculation formula is:

The uncollided neutron flux density φ ^u (r, E) is further calculated from the uncollided neutron angular flux density φ ^u (r, Ω, E), and the calculation formula is:

是中子从r_p处到达r处的运动方向，

是狄拉克函数，q是外中子点源源强，τ(r_p,r)是中子从r_p处穿行到达r处的光学距离，计算公式为：where φ ^u (r, Ω, E) is the angular flux density of uncollided neutrons, r is the spatial position, Ω is the direction of neutron motion, E is the neutron energy,

is the direction of motion of neutrons from r _p to r,

is the Dirac function, q is the source intensity of the outer neutron point source, τ(r _p , r) is the optical distance for neutrons to travel from r _p to r, and the calculation formula is:

τ(r _p ,r)＝∫ _s Σ _t ds (3)

where Σ _t is the total cross section, s is the path length of neutrons traveling from r _p to r; the first collision source Q ^c (r, Ω, E) is calculated from the angular flux density of uncollided neutrons, and the calculation formula is:

where Q ^c (r, Ω, E) is the first collision source with neutron energy E and direction Ω at spatial position r, and Σ _s (r, E′, Ω′→E, Ω) is the neutron at spatial position r Scattering cross section from energy E′ and direction Ω′ to energy E and direction Ω, χ(E) is the fission spectrum, υ is the average number of neutrons produced per fission, Σ _f (r, E′) is the neutron At the spatial position r, the fission cross section of energy E', φ(r, Ω', E') is the neutron angular flux density at the spatial position r, the energy is E', and the direction is Ω';

Step 2: Starting from the first collision source Q _c (r, Ω, E) obtained in Step 1, the Monte Carlo method is used to simulate the neutron transport process, using source bias, while reducing the distance from the target ex-core detector The weight of the first collision source is increased, and the weight of the first collision source close to the target extra-heap detector is increased, counted in the grid where the extra-heap detector is located, and the collision neutron flux density φ ^c (r ,E);

Step 3: Add the colliding neutron flux density φ ^c (r, E) at the extra-core detector to the uncollided neutron flux density φ ^u (r, E) at the extra-core detector to obtain the target detection The neutron flux density φ(r,E) at the target detector is multiplied by the neutron flux density φ(r,E) at the target detector and the response function Σ _d of the extra-core detector and integrated for energy and space, Get the response RES from the off-heap probe.

Compared with the prior art, the present invention has the following prominent advantages:

1. Compared with the Monte Carlo method, the uncollided neutron flux is calculated by the semi-analytical ray tracing method, which is a deterministic method with fast calculation speed;

2. Compared with the external neutron source distributed only in the reactor stack, the first collision source distributed in the entire reactor area has a wider distribution range. The first collision source is calculated by the Monte Carlo method, and the neutrons reaching the detector outside the reactor The number is more, and the biased sampling operation can be performed according to the spatial distribution and direction of the first collision source, which further increases the number of neutrons reaching the detector outside the core, reduces the variance of the calculation results of the Monte Carlo method, and improves the calculation efficiency.

detailed description

The invention applies the first collision source technology to the calculation of the deep penetration problem, and uses the semi-analytic ray tracing method and the Monte Carlo method for calculation. The specific calculation process of this method includes the following aspects:

Step 1: According to the material and geometric characteristics of the reactor, the reactor area is divided into the inner area including the core, reflector and shielding layer, and the outer area including the outer detector. According to the neutron flux density of the first collision source technology Divided into the uncollided neutron flux density φ ^u (r, E) and the collided neutron flux density φ ^c (r, E); firstly, the entire reactor area is divided into grids in the three-dimensional rectangular coordinate system, and the actual reactor The external neutron source is generally a volume source, and the external neutron volume source is converted into an external neutron point source located at the center of the grid in the source area. Integrating, the source intensity of the neutron point source at the center of the grid is obtained, that is, the volume source in the entire grid is equivalent to the point source at the center of the grid; starting from the outer neutron point source, the semi-analytic ray tracing method is used to calculate The uncollided flux density φ ^u (r,E) of the entire reactor region; for an external neutron point source, the semi-analytical ray tracing method is used to calculate the neutrons generated from the neutron point source r _p reaching the specified position r in space The uncollided neutron angular flux density φ ^u (r,E,Ω), the calculation formula is:

The uncollided neutron flux density φ ^u (r,E) can be further calculated from the uncollided neutron angular flux density φ ^u (r,E,Ω), and the calculation formula is:

是中子从r_p处到达r处的运动方向，

是狄拉克函数，q是外中子点源源强，τ(r_p,r)是中子从r_p处穿行到达r处的光学距离，计算公式为：where φ ^u (r,E,Ω) is the angular flux density of uncollided neutrons, Ω is the direction of neutron motion,

is the direction of motion of neutrons from r _p to r,

is the Dirac function, q is the source intensity of the outer neutron point source, τ(r _p , r) is the optical distance for neutrons to travel from r _p to r, and the calculation formula is:

τ(r _p ,r)＝∫ _s Σ _t ds (3)

where Σ _t is the total cross section, s is the path length of neutrons traveling from r _p to r; the first collision source Q ^c (r, Ω, E) is calculated from the angular flux density of uncollided neutrons, and the calculation formula is:

where Q ^c (r, Ω, E) is the first collision source with neutron energy E and direction Ω at spatial position r, and Σ _s (r, E′, Ω′→E, Ω) is the neutron at spatial position r Scattering cross section from energy E′ and direction Ω′ to energy E and direction Ω, χ(E) is the fission spectrum, υ is the average number of neutrons produced per fission, Σ _f (r, E′) is the neutron At the spatial position r, the fission cross section of energy E', φ(r, Ω', E') is the neutron angular flux density at the spatial position r, the energy is E', and the direction is Ω';

Step 2: Starting from the first collision source obtained in step 1 by the Monte Carlo method, the first collision source Q ^c (r, Ω, E) is regarded as an external neutron source, and the source bias is performed according to the spatial distribution of the first collision source, Increase the weight of the first collision source in the grid far away from the extra-heap detector, reduce the weight of the first collision source in the grid close to the extra-heap detector, and simulate the neutron transport process (5). Counting in the grid of , get the collision neutron flux density φ ^c (r,E) at the detector outside the pile;

where φ ^c (r, Ω, E) is the angular flux density of collision neutrons at space position r with neutron energy E and flight direction Ω, Σ _t is the total cross section, Σ _s (r, E′, Ω′ →E,Ω) is the scattering cross-section of neutrons scattered from energy E′ and direction Ω′ to energy E and direction Ω at spatial position r, Σ _f (r,E′) is the scattering cross section of neutrons from energy E′ at spatial position r χ(E) is the fission spectrum, υ is the average number of neutrons produced by each fission, Q ^c (r, Ω, E) is the first collision source at spatial position r, direction Ω, and energy E;

Step 3: Compare the uncollided neutron flux density φ ^u (r,E) at the extra-core detector calculated by the semi-analytical ray tracing method with the collided neutron flux at the extra-core detector calculated by the Monte Carlo method The flux density φ ^c (r, E) is added in the grid at the ex-core detector to obtain the neutron flux density φ(r, E) at the ex-core detector, and the neutron flux density at the ex-core detector The flux density is multiplied by the response function Σ _d of the detector and integrated for energy and space to obtain the response RES of the detector outside the heap. The calculation formula is:

RES = _∫∫Σd φ(r, E)dEdr (6).

Claims (1)

1. the method for acquiring the response of the detector outside the reactor based on the first collision source-Monte Carlo coupling is characterized in that: the method comprises the following steps:

step 1: according to the material and geometrical characteristics of the reactor, the reactor area is divided into an in-core area containing a reactor core, a reflecting layer and a shielding layer and an out-of-core area containing an out-of-core detector, and the neutron flux density is divided into a non-collision neutron flux density phi according to the first collision source technology ^u (r, E) and collision neutron flux density phi ^c (r, E); dividing the whole reactor region into three-dimensional rectangular coordinate system grids, taking an external neutron source in an actual reactor as a source, converting the external neutron source into an external neutron source located at the center of the source region grid, wherein the conversion mode is as follows: integrating the distribution of the source intensity of the external neutron source to the volume of the grid to obtain the source intensity of the neutron source positioned at the center of the grid, namely, the source in the whole grid is equivalent to the point source at the center of the grid; calculating the density phi of non-collision flux in the whole reactor area by using a semi-analytic ray tracing method from an external neutron point source ^u (r, E); for an external neutron source, calculating the secondary neutron source r by using a semi-analytic ray tracing method _p Angular flux density of non-colliding neutrons φ at a given position r in arrival space ^u (r, Ω, E), the calculation formula is:

from non-colliding neutrons angular flux density phi ^u (r, Ω, E) further calculating the uncontacted neutron flux density φ ^u (r, E) according to the formula:

wherein phi ^u (r, Ω, E) is the non-impinging neutron angular flux density, r is the spatial position, Ω is the neutron direction of motion, E is the neutron energy,

is neutron from r _p Where it reaches the direction of motion at r,

is the Dirac function, q is the source strength of the external neutron point source, τ (r) _p R) is neutron from r _p The optical distance from the position where the light passes to the position r is calculated by the formula:

τ(r,r _p )＝∫ _s Σ _t ds (3)

wherein _t Is the total cross section, s is the neutron from r _p The length of the path from where the beam travels to where r is reached; calculation of first-time collision source Q from non-collision neutron angular flux density ^c (r, Ω, E), the calculation formula is:

wherein Q ^c (r, Ω, E) is the first collision source with neutron energy E in direction Ω at spatial location r, Σ _s (r, E ', Ω' → E, Ω) are scattering cross sections of neutrons at spatial location r from energy E 'and direction Ω' to energy E and direction Ω, χ (E) is the fission spectrum, υ is the average number of neutrons per fission, Σ _f (r, E ') is the fission cross section of a neutron at spatial position r at energy E', and φ (r, Ω ', E') is the neutron angular flux density at spatial position r at energy E 'and direction Ω';

step 2: first collision source Q obtained from step 1 by the Monte Carlo method _c Starting from (r, omega and E), simulating the neutron transportation process, adopting source bias, simultaneously reducing the weight of a first collision source far away from a target out-of-pile detector, improving the weight of the first collision source near the target out-of-pile detector, counting grids where the out-of-pile detectors are located, and obtaining pilesCollision neutron flux density phi at the outer detector ^c (r,E)；

And 3, step 3: (iii) collisional neutron flux density phi at the out-of-pile detector ^c (r, E) and the non-collision neutron flux density at the out-of-core detector ^u (r, E) are added to obtain the neutron flux density phi (r, E) at the target detector, and the neutron flux density phi (r, E) at the target detector and the response function sigma of the out-of-pile detector are compared _d The energy and space are multiplied and integrated to obtain the response RES of the out-of-stack detector.