Calculation method for response of out-of-pile detector of VVER unit

Abstract

The invention discloses a VVER unit out-of-pile detector response calculation method, which comprises the following steps of: 1, constructing a VVER unit entity geometric model according to geometric and material arrangement information of a VVER unit core, dividing a hexagonal coarse mesh and a rectangular fine mesh for the model, and establishing a mapping relation between the hexagonal coarse mesh and the rectangular fine mesh; constructing a shielding calculation physical model; 2, executing conjugate neutron transport calculation through a three-dimensional discrete longitudinal standard method to obtain conjugate neutron flux density of each rectangular fine mesh; thirdly, merging the conjugate neutron-flux density of each rectangular fine mesh into the conjugate neutron-flux density of the corresponding hexagonal coarse mesh; fourthly, calculating a space response function of the out-of-pile detector through the conjugate neutron flux density of the hexagonal coarse mesh; and 5, calculating the response of the out-of-pile detector. The method can accurately and efficiently calculate the response of the out-of-pile detector of the VVER unit, and has industrial application value.

Description

Technical Field

[0001] The invention relates to the technical field of pressurized water reactor core physics calculation, and in particular to a method for calculating the response of an external detector of a VVER unit. Background Art

[0002] The VVER series units are pressurized water-cooled and water-moderated reactors (PWRs) with hexagonal fuel assemblies. With the increase in the number of VVER-type hexagonal fuel assembly commercial PWRs put into operation, the demand for hexagonal fuel assembly PWR nuclear design calculations is growing, which has promoted the development of nuclear power software autonomy and core physics analysis numerical calculations. The ex-pile detector is crucial for the application of dynamic rod engraving in commercial PWRs and power monitoring during normal power operation. Accurate calculation of the ex-pile detector response is of great significance to ensure the implementation of dynamic rod engraving technology and the calibration of the ex-pile detector.

[0003] The calculation methods of the ex-pile detector response are generally divided into forward transport method and conjugate transport method. The forward transport method repeatedly sets a unit source strength neutron source at different positions in the core, solves the forward neutron transport equation to obtain the neutron flux density at the position of the ex-pile detector, and combines it with the neutron response cross section of the nuclear reaction in the sensitive area of ​​the ex-pile detector to calculate the ex-pile detector response. However, the forward transport calculation is huge and the efficiency is much lower than the conjugate transport method. The conjugate transport method sets a conjugate source at the position of the ex-pile detector, and only needs to perform a conjugate neutron transport calculation once to obtain the contribution of neutrons at each position in the core to the ex-pile detector current signal, that is, the ex-pile detector spatial response function, and combines the three-dimensional fission reaction rate calculation of the core to obtain the ex-pile detector response. At present, conjugate transport calculations mainly use the discrete ordinate method and the Monte Carlo method. Some studies have conducted multi-group Monte Carlo conjugate transport calculations on VVER units to obtain the ex-core detector responses. However, the Monte Carlo calculation method based on probability theory involves large-scale neutron transport calculations, which has the disadvantages of long numerical calculation time, errors introduced by statistical fluctuations, and high cost for accurately solving the ex-core detector response calculations. Summary 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 method for calculating the response of the ex-core detector of a VVER unit. The method adopts a three-dimensional discrete ordinate method based on determinism to accurately and efficiently calculate the response of the ex-core detector of a commercial hexagonal pressurized water reactor, which has industrial application value.

[0005] In order to achieve the above objectives, the present invention is implemented by the following technical solutions:

[0006] A method for calculating the response of an external detector of a VVER unit adopts a three-dimensional discrete ordinate method to solve a conjugate neutron transport equation, and can efficiently and accurately realize the response calculation, comprising the following steps:

[0007] Step 1: Construct a VVER unit solid geometry model based on the detailed geometric dimensions and material layout information of the fuel assembly, heavy reflector, pressure vessel and external detector in the core of the VVER unit. Perform hexagonal coarse mesh division based on the hexagonal fuel assembly actually arranged in the core of the VVER unit solid geometry model. The size of each hexagonal coarse mesh is the size of a hexagonal fuel assembly. Then perform rectangular fine mesh division, establish a mapping relationship between the hexagonal coarse mesh and the rectangular fine mesh, and construct a shielding calculation physical model.

[0008] Step 2: Based on the shielding calculation physical model constructed in step 1, the response cross sections of the out-of-core detectors at different axial positions are used as conjugate sources, and the conjugate neutron transport equation is calculated using the three-dimensional discrete ordinate method to obtain the conjugate neutron flux density of each rectangular fine mesh in the core of the VVER unit;

[0009] Step 3: Based on the conjugate neutron flux density of each rectangular fine mesh in the core of the VVER unit calculated in step 2 and the mapping relationship between the hexagonal coarse mesh and the rectangular fine mesh in step 1, the conjugate neutron flux density of the rectangular fine mesh is merged into the conjugate neutron flux density of the hexagonal coarse mesh by using the volume weight method, as shown in formula (1):

[0010]

[0011] Where:

[0012] ——the conjugate neutron flux density of the g-th energy group of the i-th hexagonal coarse mesh;

[0013] ——The conjugate neutron flux density of the g-th energy group of the k-th rectangular fine mesh in the i-th hexagonal coarse mesh;

[0014] V k ——the volume of the kth fine mesh within the i-th hexagonal coarse mesh;

[0015] Step 4: According to the conjugate neutron flux density of the hexagonal coarse mesh merged in step 3, calculate the spatial response function of the ex-core detector, as shown in formula (2):

[0016]

[0017] Where:

[0018] ω i ——spatial response function of the off-pile detector of the i-th hexagonal coarse mesh;

[0019] V i ——the volume of the i-th hexagonal coarse mesh;

[0020] χ g ——fission energy spectrum of the gth energy group;

[0021] Step 5: Use the core physics calculation program to calculate the three-dimensional fission reaction rate of the VVER unit core. According to the spatial response function of the external detector calculated in step 4, the response of the external detector is obtained, as shown in formula (3):

[0022]

[0023] Where:

[0024] R——ex-pile detector response;

[0025] R f,i ——The fission reaction rate of the i-th hexagonal coarse mesh.

[0026] Preferably, when constructing a shielding calculation physical model, it is necessary to map the hexagonal coarse mesh and the rectangular fine mesh. The rectangular fine mesh of the hexagonal fuel assembly adopts a fixed size, with a length of one twentieth of the opposite side distance of the hexagonal fuel assembly and a width of one tenth of the radius of the inscribed circle of the hexagonal fuel assembly. The above size is used to ensure that the rectangular fine mesh is fine enough, thereby ensuring the calculation efficiency without affecting the calculation accuracy of the conjugate neutron transport equation.

[0027] Compared with the prior art, the present invention has the following advantages:

[0028] 1. For the VVER unit, a solid geometric model is constructed to ensure the accuracy of the physical model. The three-dimensional discrete ordinate method is used to perform conjugate neutron transport calculations to obtain the spatial response function of the ex-pile detector. The calculation speed is fast and the global conjugate neutron flux density can be obtained at one time. Compared with the traditional two-dimensional radial response function combined with the axial response function, the three-dimensional spatial response function obtained by the three-dimensional discrete ordinate method has higher calculation accuracy for the calculated ex-pile detector response.

[0029] 2. Based on the establishment of the mapping relationship between the hexagonal coarse mesh and the rectangular fine mesh, the shortcoming that the three-dimensional discrete ordinate method cannot describe the hexagonal coarse mesh is solved, and the high-precision off-pile detector response calculation based on the geometric dimensions of the hexagonal fuel assembly is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 The calculation process of the external detector response of the VVER unit;

[0031] Figure 2 Schematic diagram of the equivalent division of rectangular grids for hexagonal fuel assemblies;

[0032] Figure 3 The shielding calculation physical model is constructed for the radial schematic diagram of the position of the ex-core detector relative to the core;

[0033] Figure 4 This is a schematic diagram of the axial detectors of the out-of-core detector;

[0034] Figure 5 This is the calculation result of the first channel ex-core detector response during the power operation stage of the VVER unit.

[0035] Figure 6 This is the calculation result of the fourth channel extra-core detector response during the power operation stage of the VVER unit.

[0036] Figure 7 This is the calculation result of the seventh channel extra-core detector response during the power operation stage of the VVER unit.

[0037] Figure 8 This is the calculation result of the ninth channel extra-core detector response during the power operation stage of the VVER unit. DETAILED DESCRIPTION

[0038] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0039] The present invention adopts the conjugate transport method to calculate the response of the VVER unit's external detector. The specific steps are as follows: Figure 1 As shown, the following steps are included:

[0040] Step 1: Construct a VVER unit solid geometry model based on the detailed geometric dimensions and material layout information of the fuel assembly, heavy reflector, pressure vessel and external detector in the core of the VVER unit. Perform hexagonal coarse mesh division based on the hexagonal fuel assembly actually arranged in the core of the VVER unit solid geometry model. The size of each hexagonal coarse mesh is the size of a hexagonal fuel assembly. Then perform rectangular fine mesh division. The rectangular fine mesh size adopts a fixed size, with a length of one twentieth of the opposite side distance of the hexagonal fuel assembly and a width of one tenth of the radius of the inscribed circle of the hexagonal fuel assembly. Establish a mapping relationship between the hexagonal coarse mesh and the rectangular fine mesh as shown in the following figure: Figure 2 As shown; the shielding calculation physical model is constructed, and the schematic diagram from the VVER unit core fuel assembly to the external detector is as follows Figure 3 As shown, the core fuel assembly, heavy reflector, pressure vessel and external detector are arranged in sequence from inside the reactor to outside the reactor.

[0041] Step 2: Based on the shielding calculation physical model constructed in step 1, the response cross sections of the external detectors at different axial positions are taken as conjugate sources, and the conjugate neutron transport equation is calculated using the three-dimensional discrete ordinate method to obtain the conjugate neutron flux density of each rectangular fine mesh in the core of the VVER unit; the schematic diagram of the axial position of the external detector relative to the core is shown in Figure 4 As shown, three detectors are arranged axially.

[0042] Step 3: Based on the conjugate neutron flux density of each rectangular fine mesh in the core of the VVER unit calculated in step 2 and the mapping relationship between the hexagonal coarse mesh and the rectangular fine mesh in step 1, the conjugate neutron flux density of the rectangular fine mesh is merged into the conjugate neutron flux density of the hexagonal coarse mesh by using the volume weight method, as shown in formula (1):

[0043]

[0044] Where:

[0045] ——the conjugate neutron flux density of the g-th energy group of the i-th hexagonal coarse mesh;

[0046] ——The conjugate neutron flux density of the g-th energy group of the k-th rectangular fine mesh in the i-th hexagonal coarse mesh;

[0047] V k ——The volume of the kth rectangular fine mesh within the i-th hexagonal coarse mesh;

[0048] Step 4: According to the conjugate neutron flux density of the hexagonal coarse mesh merged in step 3, calculate the spatial response function of the ex-core detector, as shown in formula (2):

[0049]

[0050] Where:

[0051] ω i ——spatial response function of the off-pile detector of the i-th hexagonal coarse mesh;

[0052] V i ——the volume of the i-th hexagonal coarse mesh;

[0053] χ g ——fission energy spectrum of the gth energy group;

[0054] Step 5: Use the core physics calculation program SPARK to calculate the three-dimensional fission reaction rate of the VVER unit core. According to the spatial response function of the external detector calculated in step 4, the response of the external detector is obtained, as shown in formula (3):

[0055]

[0056] Where:

[0057] R——ex-pile detector response;

[0058] R f,i ——The fission reaction rate of the i-th hexagonal coarse mesh.

[0059] Figure 5 , Figure 6 , Figure 7 and Figure 8 They are the response calculation values ​​of the ex-core detectors in the first channel, the fourth channel, the seventh channel and the ninth channel of the VVER unit, respectively. In the power operation stage, the response calculation values ​​of the ex-core detectors in the four channels have the same change trend as the power measured values. Therefore, the method of the present invention is suitable for the response calculation of the ex-core detectors of the VVER unit and has industrial application value.

Claims

1. A method for calculating the response of an external detector of a VVER unit, characterized by: The following steps are involved: Step 1: Construct a VVER unit solid geometry model based on the detailed geometric dimensions and material layout information of the fuel assembly, heavy reflector, pressure vessel and external detector in the core of the VVER unit. Perform hexagonal coarse mesh division based on the hexagonal fuel assembly actually arranged in the core of the VVER unit solid geometry model. The size of each hexagonal coarse mesh is the size of a hexagonal fuel assembly. Then perform rectangular fine mesh division, establish a mapping relationship between the hexagonal coarse mesh and the rectangular fine mesh, and construct a shielding calculation physical model. Step 2: Based on the shielding calculation physical model constructed in step 1, the response cross sections of the out-of-core detectors at different axial positions are used as conjugate sources, and the conjugate neutron transport equation is calculated using the three-dimensional discrete ordinate method to obtain the conjugate neutron flux density of each rectangular fine mesh in the core of the VVER unit; Step 3: Based on the conjugate neutron flux density of each rectangular fine mesh in the core of the VVER unit calculated in step 2 and the mapping relationship between the hexagonal coarse mesh and the rectangular fine mesh in step 1, the conjugate neutron flux density of the rectangular fine mesh is merged into the conjugate neutron flux density of the hexagonal coarse mesh by using the volume weight method, as shown in formula (1): Where: ——the conjugate neutron flux density of the g-th energy group of the i-th hexagonal coarse mesh; ——The conjugate neutron flux density of the g-th energy group of the k-th rectangular fine mesh in the i-th hexagonal coarse mesh; V k ——the volume of the kth fine mesh within the i-th hexagonal coarse mesh; Step 4: According to the conjugate neutron flux density of the hexagonal coarse mesh merged in step 3, calculate the spatial response function of the ex-core detector, as shown in formula (2): Where: ω i ——spatial response function of the off-pile detector of the i-th hexagonal coarse mesh; V i ——the volume of the i-th hexagonal coarse mesh; χ g ——fission energy spectrum of the gth energy group; Step 5: Use the core physics calculation program to calculate the three-dimensional fission reaction rate of the VVER unit core. According to the spatial response function of the external detector calculated in step 4, the response of the external detector is obtained, as shown in formula (3): Where: R——ex-pile detector response; R f,i ——The fission reaction rate of the i-th hexagonal coarse mesh.

2. The method for calculating the response of an external detector of a VVER unit according to claim 1, characterized in that: When constructing the shielding calculation physical model, it is necessary to map the hexagonal coarse mesh and the rectangular fine mesh. The rectangular fine mesh of the hexagonal fuel assembly adopts a fixed size, with a length of one twentieth of the opposite side distance of the hexagonal fuel assembly and a width of one tenth of the radius of the inscribed circle of the hexagonal fuel assembly.

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