Method for parameterizing few group constants with state parameters including xenon concentration

Abstract

The invention discloses a few-group constant parameterization method with state parameters including xenon concentration, which comprises the following steps: taking Xe concentration as a state parameter, selecting a physical quantity of the Xe concentration state parameter, designing an Xe concentration state matrix, and carrying out component trunk and branch calculation on the basis; determining a combination mode of Xe concentration and other state parameters, dividing the combination mode into different subitems, selecting a function form and a fitting order, functionalizing the different subitems respectively, and making a few group constant library; in the reactor core calculation process, interpolation is carried out in the few-group constant library through Xe concentration back substitution to obtain a few-group cross section for subsequent calculation of the reactor core. According to the method, the number of working condition points for manufacturing the few-group constant library can be reduced, the two-step program component calculation speed is increased, and meanwhile the reactor core calculation precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of nuclear reactor core physical analysis, and particularly relates to a few-group constant parameterization method with state parameters including xenon concentration. Background Art

[0002] The core physical analysis software of a pressurized water reactor plays a key role in multiple processes such as core design, operation analysis, and safety review of commercial pressurized water reactor nuclear power plants. The two-step method is widely used in existing core physical analysis software for pressurized water reactors. In this method, a series of discrete operating conditions of given state parameters of the assembly are first calculated to obtain few-group constants, and then these discrete few-group constants under a finite number of operating conditions are functionalized to obtain the continuous functional relationship between the few-group constants and the state parameters, forming a few-group constant library; during the core calculation process, directly based on this few-group constant library, according to the state parameters and in the actual operating conditions of the core, function substitution calculation is performed to obtain the required few-group constants online.

[0003] In the above process, the process of obtaining the corresponding continuous functional relationship through functionalization based on the discrete correspondence between the few-group constants and the state parameters, and obtaining the few-group constants through parameter substitution in the core calculation is called few-group constant parameterization. Among them, all the discrete operating conditions used in the assembly calculation will form a state matrix; the process of obtaining the continuous functional relationship based on the discrete correspondence is called functionalization; in the core calculation, the process of obtaining the actual few-group constants according to the current actual state parameter values based on the continuous functional relationship stored in the few-group constant library is called parameter substitution.

[0004] In the existing core physical analysis technology for pressurized water reactors, the commonly used state parameters include burnup depth (Bu), boron concentration (CB), fuel effective temperature (TF), moderator temperature (TM), etc. For important nuclides such as Xe and Sm, a microscopic burnup model is often used, that is, the few-group constants given by the assembly calculation include data such as the microscopic cross-section and yield of important nuclides. During the core calculation, according to the actual operation process, the nuclide concentration is calculated online, and then together with the microscopic cross-section, it is re-entered into the macroscopic cross-section to affect the neutron transport / diffusion process. The macroscopic cross-sections used in this processing method are all values at the equilibrium Xe concentration, only considering the direct influence of the nuclide concentration and not considering its indirect influence through affecting the neutron energy spectrum and energy group merging.

[0005] However, during the operation of the reactor core, the concentration of the poison Xe will change rapidly within a short time due to the change in flux. Because of its large absorption cross-section, it will cause a significant neutron energy spectrum hardening effect, which is quite different from the equilibrium Xe concentration state and cannot be ignored. On the one hand, in order to characterize the influence at the beginning of the reactor core cycle, generally in the component burnup calculation process, a transient Xe model is adopted for component calculation, that is, the change in Xe concentration is actually considered, but the step size of the burnup depth value must be greatly encrypted, significantly increasing the discrete operating points and wasting computing resources. On the other hand, the influence of the change in Xe concentration on the neutron energy spectrum at non-initial cycle conditions cannot be considered, which will cause calculation errors at the theoretical source. Especially in the cases of severe control rod insertion and extraction, xenon oscillation, etc., the xenon concentration in the reactor core is quite different from the xenon concentration in the component calculation. Summary of the Invention

[0006] In order to overcome the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a few-group constant parameterization method with state parameters including Xe concentration. Taking Xe concentration as a state parameter, a state matrix is designed for component calculation; during the reactor core calculation process, through the back substitution of Xe concentration, the full quantitative influence of it on the macroscopic few-group constants is obtained. From the theoretical method, the speed of component calculation in the two-step method is improved, and the accuracy of reactor core calculation is also improved.

[0007] In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0008] A few-group constant parameterization method with state parameters including Xe concentration, comprising the following steps:

[0009] Step 1: Select the physical quantities of the Xe concentration state parameter, including the absolute value of Xe concentration and the relative proportion of the absolute value of Xe concentration relative to the reference value, where the reference value of Xe concentration is taken as the equilibrium concentration at the specified burnup depth;

[0010] Step 2: Design the Xe concentration state matrix. The minimum and maximum value intervals of the discrete operating conditions of Xe concentration should cover all possible Xe concentrations in the reactor core calculation, using the range from zero to the peak value of xenon oscillation at full power of the reactor core, and the number of discrete operating conditions of Xe concentration should be as small as possible and meet the requirement that the subsequent functional back substitution verification error is less than 0.2%;

[0011] Step 3: Use the Xe concentration state matrix designed in Step 2 for component calculation, including the main calculation for burnup calculation and the branch calculation for adjusting state parameters based on the main calculation; first, perform burnup calculation on the basis of the selected burnup depth sequence to obtain the few-group constants in the main state; then, based on the main calculation, change the Xe concentration to other values of the discrete operating conditions of Xe concentration in Step 2 to obtain the few-group constants in the branch state;

[0012] Step 4: Determine the combined form of Xe concentration and other state parameters that will affect the calculation results of few-group constants. The other state parameters include burnup depth, boron concentration, moderator temperature, and fuel temperature. Group the state parameters according to the physical mechanism of the coupling effect between the state parameters. Each group is a sub-item that affects the few-group constants, and functionalization is completed within each group. The functionalization method uses a polynomial function with a simple form and easy implementation in numerical calculations. The specific numerical implementation method uses least squares fitting. On this basis, further determine the fitting order of each state parameter, where the Xe concentration is first-order fitting:

[0013] Σ = f base (BU, CB)·Δf(Xe) + Δf(CB, Tf, Tm)

[0014] In the formula:

[0015] Σ —— represents the macroscopic cross-section;

[0016] f base —— the basic term of the few-group constant;

[0017] BU —— represents the burnup depth;

[0018] CB —— represents the boron concentration;

[0019] Δf —— the correction term of the few-group constant;

[0020] Xe —— represents the nuclear number density of Xe;

[0021] Tf —— represents the fuel temperature;

[0022] Tm —— represents the moderator temperature

[0023] After determining the combination of Xe concentration and other state parameters, the hardening effect of the neutron energy spectrum caused by the rapid increase of Xe concentration when the core burnup depth is less than 150 MWd / tU can be effectively considered. There is no need to select too fine segmentation of burnup and division of burnup points to depict the process of gradual hardening of the neutron energy spectrum;

[0024] Step 5: After determining the combined form and fitting order through Step 4, perform functionalization calculations to create a few-group constant library. Obtain the Xe concentration under actual working conditions in the core calculation, and substitute it back into the few-group constant library to obtain the core macroscopic cross-section for subsequent calculations. Among them, the physical quantity for substituting and calculating the Xe concentration needs to be consistent with the physical quantity selected in Step 1.

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

[0026] 1. When the parametric process state parameter includes the Xe concentration, it can effectively consider the hardening effect of the neutron energy spectrum caused by the rapid increase in the Xe concentration when the core burnup depth is less than 150 MWd / tU. Compared with the parametric method where the state parameter does not include the Xe concentration, the method of the present invention does not need to select overly fine burnup segmentation and burnup point division to depict the gradually hardening process of the neutron energy spectrum, reducing the number of burnup segments and burnup points and thus reducing the calculation amount.

[0027] 2. When the core xenon concentration does not deviate from the assembly-calculated xenon concentration, this method can maintain the same accuracy as the parametric method without xenon concentration in the state parameter while reducing the calculation amount.

[0028] 3. When the core xenon concentration deviates from the assembly-calculated xenon concentration, this method can consider the hardening effect of the energy spectrum caused by the difference in xenon concentration between the assembly and the core. Description of the Drawings

[0029] Figure 1 It is a comparison of the results of the infinite multiplication factors calculated by two parametric methods (whether the state parameter includes the Xe concentration) for a case where the core consists of only a single assembly under the operating condition of 100% relative power.

[0030] Figure 2 It is a comparison of the results of the infinite multiplication factors calculated by two parametric methods (whether the state parameter includes the Xe concentration) for a case where the core consists of only a single assembly under the operating condition of 1% relative power. Detailed Embodiment

[0031] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments:

[0032] A few-group constant parametric method with a state parameter including xenon concentration includes the following steps:

[0033] Step 1: Select the physical quantities of the Xe concentration state parameter, including the absolute value of the Xe concentration and the relative proportion of the absolute value of the Xe concentration relative to the reference value, where the reference value of the Xe concentration is taken as the equilibrium concentration at a specified burnup depth.

[0034] Step 2: Design the Xe concentration state matrix. The minimum and maximum intervals of the discrete operating conditions of the Xe concentration should cover all possible Xe concentrations in core calculations, using the range from zero to the peak of xenon oscillation at full core power. And the number of discrete operating conditions of the Xe concentration should be as small as possible and ensure that the subsequent functional back-substitution verification error is less than 0.2%.

[0035] Step 3: Use the Xe concentration state matrix designed in Step 2 to perform component calculations, including the main calculation for burnup calculation and the branch calculation for adjusting state parameters based on the main calculation; first perform burnup calculation on the basis of the selected burnup depth sequence to obtain the few-group constants in the main state; then, based on the main calculation, change the Xe concentration to other values in the Xe concentration discrete conditions in Step 2 to obtain the few-group constants in the branch state;

[0036] Step 4: Determine the combination form of Xe concentration and other state parameters (burnup depth, boron concentration, moderator temperature, and fuel temperature) that will affect the calculation results of few-group constants; group the state parameters according to the physical mechanism of the coupling effect between state parameters, and each group is a sub-item that affects the few-group constants, and functionalization is completed within each group; the functionalization method uses a polynomial function with a simple form and easy implementation in numerical calculations, and the specific implementation numerical scheme method uses least squares fitting; on this basis, further determine the fitting order of each state parameter, for example, the Xe concentration is a first-order fitting:

[0037] Σ = f base (BU, CB)·Δf(Xe) + Δf(CB, Tf, Tm)

[0038] In the formula:

[0039] Σ —— represents the macroscopic cross section;

[0040] f base —— the basic term of the few-group constant;

[0041] BU —— represents the burnup depth;

[0042] CB —— represents the boron concentration;

[0043] Δf —— the correction term of the few-group constant;

[0044] Xe —— represents the nuclear number density of Xe;

[0045] Tf —— represents the fuel temperature;

[0046] Tm —— represents the moderator temperature

[0047] After determining the combination of Xe concentration and other state parameters, the hardening effect of the neutron energy spectrum caused by the rapid increase of Xe concentration when the core burnup depth is less than 150 MWd / tU can be effectively considered, and there is no need to select overly detailed burnup segmentation and burnup point division to depict the process of gradual hardening of the neutron energy spectrum; compared with the parameterization method where the state parameters do not include Xe concentration, this method can effectively reduce the number of burnup segments and burnup points;

[0048] Step 5: After determining the combination form and fitting order through Step 4, perform functional calculation to create a few-group constant library; obtain the Xe concentration under actual conditions in core calculation, and substitute it back into the few-group constant library to obtain the core macroscopic cross section for subsequent calculations; among them, the physical quantity for substituting and calculating the Xe concentration needs to be consistent with the physical quantity selected in Step 1.

[0049] The method of the present invention is verified as follows:

[0050] Figure 1 It is a comparison of the results of the infinite multiplication factors calculated by two parameterization methods (whether the state parameters include the Xe concentration) for a case where the core consists of only a single assembly under the operating condition of 100% relative power. Since the relative power is 100%, the Xe concentration in the single assembly in the core is consistent with that in the discrete conditions of the assembly calculation. Therefore, the calculation results of the two parameterizations are not much different, indicating that when the core Xe concentration does not deviate from the assembly calculation Xe concentration, the method of the present invention can maintain the same accuracy as the parameterization method that does not consider the Xe concentration while reducing the calculation amount.

[0051] Figure 2 It is a comparison of the results of the infinite multiplication factors calculated by two parameterization methods (whether the state parameters include the Xe concentration) for a case where the core consists of only a single assembly under the operating condition of 1% relative power. Since the relative power is 1%, the Xe concentration in the single assembly in the core is quite different from that in the discrete conditions of the assembly calculation. The parameterization method with state parameters including the Xe concentration can consider the neutron energy spectrum hardening effect caused by the large difference in Xe concentration. There are differences in the calculation results of the two parameterization methods, indicating that when the core Xe concentration deviates from the assembly calculation Xe concentration, the method of the present invention can consider the energy spectrum hardening effect caused by the different Xe concentrations in the assembly and the core.

Claims

1. A few-group constant parameterization method with state parameters including xenon concentration, characterized in that: It includes the following steps: Step 1: Select the physical quantities of the Xe concentration status parameter, including the absolute value of the Xe concentration and the relative proportion of the absolute value of the Xe concentration relative to the reference value, where the reference value of the Xe concentration is taken as the equilibrium concentration at the specified burnup depth; Step 2: Design the Xe concentration status matrix. The minimum and maximum intervals of the discrete working conditions of the Xe concentration should cover all possible Xe concentrations in the core calculations, using the value from zero to the peak of the xenon oscillation at full power of the core. And the number of discrete working conditions of the Xe concentration should be as small as possible and ensure that the subsequent functionalized back substitution verification error is less than 0.2%; Step 3: Use the Xe concentration status matrix designed in Step 2 to perform assembly calculations, including the main calculation for burnup calculation and the branch calculation for adjusting the status parameter based on the main calculation; First, perform burnup calculation based on the selected burnup depth sequence to obtain the few-group constants in the main state; Then, based on the main calculation, change the Xe concentration to other values of the discrete working conditions of the Xe concentration in Step 2 to obtain the few-group constants in the branch state; Step 4: Determine the combination form of the Xe concentration and other status parameters that will affect the calculation results of the few-group constants. Other status parameters include burnup depth, boron concentration, moderator temperature, and fuel temperature; According to the physical mechanism of the coupling effect between status parameters, group the status parameters. Each group is an item that affects the few-group constants, and functionalization is completed within each group; The functionalization method uses a polynomial function with a simple form and easy to implement in numerical calculations. The specific numerical implementation method uses least squares fitting; On this basis, further determine the fitting order of each status parameter, where the Xe concentration is a first-order fitting: Σ = f base (BU, CB)·Δf(Xe) + Δf(CB, Tf, Tm) In the formula: Σ —— represents the macroscopic cross section; f base —— Fundamental term of a few group constants; BU —— represents the burnup depth; CB —— represents the boron concentration; Δf —— represents the correction term of the few-group constant; Xe —— represents the nuclear number density of Xe; Tf —— represents the fuel temperature; Tm —— represents the moderator temperature After determining the combination of the Xe concentration and other status parameters, it is possible to effectively consider the hardening effect of the neutron energy spectrum caused by the rapid increase in the Xe concentration when the core burnup depth is less than 150 MWd / tU, without the need to select overly fine burnup segmentation and burnup point division to depict the process of gradual hardening of the neutron energy spectrum; Step 5: After determining the combination form and fitting order through Step 4, perform functionalized calculations to create a few-group constant library; Obtain the Xe concentration under the actual working conditions in the core calculation and substitute it back into the few-group constant library to obtain the core macroscopic cross section for subsequent calculations; Among them, the physical quantity for substituting and calculating the Xe concentration needs to be consistent with the physical quantity selected in Step 1.

Images