Discrete segment integral coefficient calculation method suitable for strong inhomogeneous medium neutron transport calculation

Abstract

The invention provides a discrete node integral coefficient calculation method suitable for strong inhomogeneous medium neutron transport calculation. The discrete node integral coefficient calculation method comprises the following steps: determining a neutron light thickness parameter; the medium is divided into a black body area, a light thickness area, a light thinning area and a vacuum area according to the size of the neutron light thickness parameter; and calculating the integral coefficient of each discrete segment for the black body region, the light thickness region, the light thinning region and the vacuum region by adopting different methods. According to the method, the problem of neutron transport calculation distortion of the strong inhomogeneous medium caused by limited factor value precision of a traditional method can be avoided.

Description

Technical Field

[0001] The invention relates to the field of numerical simulation of neutron transport process in nuclear engineering, and in particular to a discrete nodal integral coefficient calculation method suitable for neutron transport calculation in strongly inhomogeneous media. Background Art

[0002] In the field of nuclear engineering, especially in the design and operation of fast neutron reactors, numerical simulation of neutron transport is crucial. However, due to the extremely complex physical characteristics inside the reactor, directly solving the neutron transport of the entire core is not only computationally intensive, but also often difficult to achieve. Therefore, a more feasible method is to adopt a two-step method, that is, first calculate the homogenization group constants of different components in the core, and then perform component homogenization calculations for the entire core based on these constants.

[0003] As a fast and high-precision solution method, the Discrete Nodal Transport Method has been widely used in fast reactor core transport calculations in recent years. However, when faced with strongly inhomogeneous media, the traditional discrete nodal method will have large errors in calculating the integral coefficients, resulting in distortion or even failure of neutron transport calculations. Therefore, how to improve the calculation method of the discrete nodal integral coefficients to meet the needs of neutron transport calculations in strongly inhomogeneous media has become a problem that needs to be solved urgently. Contents of the invention

[0004] In order to overcome the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a discrete block integral coefficient calculation method suitable for neutron transport calculation in strongly inhomogeneous media. This method expands the scope of application of the existing discrete block method and enables it to be effectively applied to the increasingly important strongly inhomogeneous core neutron transport calculation problem.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A discrete nodal integral coefficient calculation method suitable for neutron transport calculation in strongly inhomogeneous media comprises the following steps:

[0007] Determine the neutron light thickness parameter;

[0008] According to the size of neutron optical thickness parameter, the medium is divided into black body region, optical thick region, optical sparse region and vacuum region;

[0009] Different methods are used to calculate the integral coefficients of each discrete node for the black body area, light thick area, light sparse area and vacuum area.

[0010] Furthermore, the determination of the neutron light thickness parameter is specifically as follows:

[0011] According to the discrete block integral coefficient formula, a group of parameters at the e index position is defined as the neutron light thickness parameters, and the formula is:

[0012]

[0013] in, is the neutron light thickness parameter, ∑ t is the total neutron reaction cross section, h x is the mesh geometry parameter along the feature direction x, is the cosine of the angle between the neutron flight direction m and the characteristic direction x.

[0014] Furthermore, the specific criteria for the medium partition are:

[0015] The neutron light thickness parameter of the black body area is greater than or equal to a preset large value threshold; the neutron light thickness parameter of the optically thick area is greater than 1 and less than the large value threshold; the neutron light thickness parameter of the optically sparse area is greater than 0 and less than or equal to 1; the neutron light thickness parameter of the vacuum area is less than or equal to a preset small value threshold.

[0016] Furthermore, the discrete node integral coefficients for calculating the bold area are specifically:

[0017] For the blackbody region, the neutron light thickness parameter is truncated to a single large value p max , this large value guarantees The floating point number limit of the computer is not exceeded, and then the analytical expression of the integral coefficient is derived. Computer programming is performed based on the analytical expression to calculate the discrete block integral coefficient.

[0018] Furthermore, the discrete node integral coefficients for calculating the optically thick region are specifically:

[0019] For the optically thick region, the analytical expression of the integral coefficient is directly derived, and computer programming is performed based on the analytical expression to calculate the discrete node integral coefficient.

[0020] Furthermore, the discrete node integral coefficients for calculating the light sparse area are specifically:

[0021] For the optically thick region, a numerical integral formula is constructed, and computer programming is performed based on the numerical integral formula to calculate discrete nodal integral coefficients.

[0022] Furthermore, the discrete node integral coefficients for calculating the vacuum area are specifically:

[0023] The neutron light thickness parameter is truncated to a single small value, and a numerical integral formula is constructed. Computer programming is performed based on the numerical integral formula to calculate discrete block integral coefficients.

[0024] Furthermore, the method further comprises a step of computer programming implementation, that is, based on the analytical expression and the numerical integral expression, a computer program is written to calculate the integral coefficient of each discrete node.

[0025] Compared with the prior art, the present invention has the following advantages:

[0026] 1. For the core problem with rarefied optical medium, the discrete node integral coefficients calculated by the present invention can ensure the correct convergence of the discrete node neutron transport calculation;

[0027] 2. For the core problem with strong absorption and particularly large optical thickness parameters, the use of the present invention to calculate the discrete node integral coefficient can ensure the correct convergence of the discrete node neutron transport calculation.

[0028] 3. For the problem of strong non-uniform core with different light storage thickness, the invention is used to calculate the discrete block integral coefficient to ensure the correct convergence of the discrete block neutron transport calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The accompanying drawings generally illustrate various embodiments by way of example and not limitation, and together with the description and claims, serve to illustrate the embodiments of the invention. Where appropriate, the same reference numerals are used throughout the drawings to refer to the same or similar parts. Such embodiments are illustrative and are not intended to be exhaustive or exclusive embodiments of the present apparatus or method.

[0030] Figure 1 Shows when h x =1 and Time (optically rarefied medium) integrated function f j (x) The graph changes with x;

[0031] Figure 2 Shows when h r =1 and When (optically thick medium) the integrand function f j (x) The graph changes with x;

[0032] Figure 3 A schematic flow chart of the method of the present invention is shown. DETAILED DESCRIPTION

[0033] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0034] The embodiment of the present invention provides a discrete nodal integral coefficient calculation method applicable to neutron transport calculation in a strongly inhomogeneous medium, the main contents of which include:

[0035] 1. Determine the neutron light thickness parameter: According to the discrete block integral coefficient formula, find the neutron light thickness parameter that can quantify the medium inhomogeneity;

[0036] 2. Medium partition: According to the size of the neutron light thickness parameter, each grid is divided into the following areas: black body area, light thick area, light sparse area and vacuum area relative to each neutron flight direction and characteristic direction;

[0037] 3. Partition processing: For the blackbody area, the neutron optical thickness parameter is truncated to a single large value, and the analytical expression of the integral coefficient is derived. For the optically thick area, the analytical expression of the integral coefficient is directly derived. For the optically sparse area, a numerical integral expression is constructed. For the vacuum area, the neutron optical thickness parameter is truncated to a single small value, and a numerical integral expression is constructed. Computer programming is performed based on the above analytical and numerical integral expressions to calculate the integral coefficients of each discrete block, which can avoid the distortion problem of neutron transport calculation in strongly inhomogeneous media caused by limited numerical accuracy of traditional methods.

[0038] For the optical thickness parameter, according to the discrete block integral coefficient formula, a group of parameters at the e index position are defined as the neutron optical thickness parameter. The neutron optical thickness parameter is only and must be related to the total neutron reaction cross section, grid geometry parameters and angle cosine. Its typical form is: in is the neutron light thickness parameter, ∑ t is the total neutron reaction cross section, h x is the mesh geometry parameter along the feature direction x, is the cosine of the angle between the neutron flight direction m and the characteristic direction x.

[0039] For medium partitioning, the following thresholds are recommended: a single maximum value of 500 is used to determine the black body area; The dividing line is 1, and the single minimum value for determining the vacuum area is 10 -5 .

[0040] Different methods are used to calculate the integral coefficients for different regions, so as to obtain high-precision values ​​under limited numerical precision. For the blackbody region, the neutron light thickness parameter is truncated to a single large value p max , this large value should ensure Do not exceed the floating-point limit of the computer, and then derive the analytical expression of the integral coefficient. For the optically thick area, directly derive the analytical expression of the integral coefficient. For the optically sparse area, if an analytical expression is constructed, an extremely small number will appear in the denominator, resulting in a large numerical error, and this will not happen in numerical integration. Therefore, a numerical integral expression is constructed. For the vacuum area, the neutron optical thickness parameter is theoretically 0, but this may cause some large vacuum areas to not converge. Therefore, the neutron optical thickness parameter is truncated to a single small value, which is close to 0, and then a numerical integral expression is constructed. Computer programming is performed based on the above analytical and numerical integral expressions to calculate the integral coefficients of each discrete block.

[0041] The above discrete node integral coefficient calculation method has been implemented through computer program, which proves its correctness and effectiveness.

[0042] How to select neutron beam thickness parameters The definition threshold is determined so as to reasonably partition the calculation. The detailed analysis is as follows.

[0043] First, we examine the calculation effects of different integral calculation methods. The following is the integrand of the integral in formula (1):

[0044]

[0045] Figure 1 Given when h x =1 and Time (optically rarefied medium) integrated function f j (x) The graph of the change with x, Figure 2 Given when h r =1 and When (optically thick medium) the integrand function f j (x) The graph of the integrand function changes with x, and it can be seen that the graphs of the integrand function in the two cases are obviously different. When the fraction is very small or even 0, a minimum value appears in the denominator of the analytical expression. The analytical integral formula will fail. Numerical integration can avoid the denominator. For the case of The same applies to very small or even zero media. In order to avoid a large amount of When the value is 0, the value may be unstable. It is recommended to The case is uniformly truncated to 10 -5 However, when When the integrand is large, the integrand often has a strong mutation, the error of numerical integration is large or many points are needed to obtain reasonable accuracy. In this case, the analytical expression is effective. Therefore, a limit p can be defined. na ,when When numerical integration is used, When , the analytical expression is used. hour, Only when the value is extremely small will it appear, so we take p na =1.

[0046] For the optically sparse medium and optically thick medium problems, the deviations of the integral values ​​calculated by MATLAB's int function, the values ​​calculated by the analytical integral formula and the MATLAB calculated values, and the deviations of the values ​​calculated by the Gauss-Legendre numerical integral of 8 points (16 points in total) in two regions and the MATLAB calculated values ​​are shown in Tables 1 and 2. Since MATLAB has high numerical accuracy and uses advanced integration techniques, the values ​​calculated by MATLAB can be considered as reference solutions. It can be seen that for optically sparse media, the numerical integration accuracy is high and the analytical integration accuracy is poor, while for optically thick media, the opposite is true, which is consistent with the previous inference.

[0047] When If we continue to increase, the analytical expression The floating point limit of the computer will be exceeded therefore Should meet:

[0048]

[0049] The actual calculation requires computer programming to calculate the final value of the analytical expression. However, the floating-point numbers of computers are limited in precision. Most existing computer programs and compilers can support double-precision real numbers well, but the support for higher precision is limited and the calculation efficiency is low. Considering that the maximum limit of double-precision floating-point numbers is about 1.79×10 308 , Recommended It has the physical meaning of the mean free path of neutrons. When the mean free path of neutrons reaches 500, it corresponds to an extremely strong absorber, or black body. Further increase in effect will be Close, take

[0050] Table 1

[0051]

[0052]

[0053] Table 2

[0054]

[0055] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A discrete nodal integral coefficient calculation method suitable for neutron transport calculation in strongly inhomogeneous media, characterized in that: The steps include: Determine the neutron light thickness parameter; According to the size of neutron optical thickness parameter, the medium is divided into black body region, optical thick region, optical sparse region and vacuum region; Different methods are used to calculate the integral coefficients of each discrete node for the black body area, light thick area, light sparse area and vacuum area.

2. The discrete nodal integral coefficient calculation method for neutron transport calculation in strongly inhomogeneous media according to claim 1 is characterized in that: The specific method for determining the neutron light thickness parameter is as follows: According to the discrete block integral coefficient formula, a group of parameters at the e index position is defined as the neutron light thickness parameters, and the formula is: in, is the neutron light thickness parameter, ∑ t is the total neutron reaction cross section, h x is the mesh geometry parameter along the feature direction x, is the cosine of the angle between the neutron flight direction m and the characteristic direction x.

3. The discrete nodal integral coefficient calculation method for neutron transport calculation in strongly inhomogeneous media according to claim 1 is characterized in that: The specific criteria for the media partition are: The neutron light thickness parameter of the black body area is greater than or equal to a preset large value threshold; the neutron light thickness parameter of the optically thick area is greater than 1 and less than the large value threshold; the neutron light thickness parameter of the optically sparse area is greater than 0 and less than or equal to 1; the neutron light thickness parameter of the vacuum area is less than or equal to a preset small value threshold.

4. The discrete nodal integral coefficient calculation method for neutron transport calculation in strongly inhomogeneous media according to claim 1, characterized in that: The discrete node integral coefficients for calculating the black area are specifically: For the blackbody region, the neutron light thickness parameter is truncated to a single large value p max , this large value guarantees The floating point number limit of the computer is not exceeded, and then the analytical expression of the integral coefficient is derived. Computer programming is performed based on the analytical expression to calculate the discrete block integral coefficient.

5. The discrete nodal integral coefficient calculation method for neutron transport calculation in strongly inhomogeneous media according to claim 1, characterized in that: The discrete node integral coefficients for calculating the optical thick area are specifically: For the optically thick region, the analytical expression of the integral coefficient is directly derived, and computer programming is performed based on the analytical expression to calculate the discrete node integral coefficient.

6. The discrete nodal integral coefficient calculation method for neutron transport calculation in strongly inhomogeneous media according to claim 1, characterized in that: The discrete node integral coefficients for calculating the light-sparse area are specifically: For the optically thick region, a numerical integral formula is constructed, and computer programming is performed based on the numerical integral formula to calculate discrete nodal integral coefficients.

7. The discrete nodal integral coefficient calculation method for neutron transport calculation in strongly inhomogeneous media according to claim 1, characterized in that: The discrete node integral coefficients for calculating the vacuum region are specifically: The neutron light thickness parameter is truncated to a single small value, and a numerical integral formula is constructed. Computer programming is performed based on the numerical integral formula to calculate discrete block integral coefficients.

8. The method according to any one of claims 1 to 7, characterized in that The method further comprises a step of implementing by computer programming, that is, writing a computer program to calculate the integral coefficient of each discrete node based on the analytical expression and the numerical integral expression.

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