Method for calculating core power of pressurized water reactor with decay power released slowly

Abstract

A method for calculating core power of a pressurized water reactor with decay power delayed release comprises the following steps: calculating a decay power delayed release function on the basis of a fission product distribution spectrum generated by fission of fission nuclide, and calculating core delayed decay power by using core power historical data and fission nuclide section information. Therefore, an existing decay power instant release method is improved into a decay power slow release method in a power calculation strategy of a pressurized water reactor two-step calculation program NECP-Bambo, and new reactor core relative power density distribution and flux density distribution are calculated on the basis of the improved power calculation strategy. According to the method, the power calculation strategy of the two-step calculation program NECP-Bambo of the pressurized water reactor can be improved, and the calculation requirements of reactor core relative power density distribution and flux density distribution with higher precision are met.

Description

Technical Field

[0001] The invention relates to the technical field of reactor physics calculation, and in particular to a method for calculating core power of a pressurized water reactor with slow decay power release. Background Art

[0002] PWR core analysis software plays a key role in the core design, operation analysis, safety review and other processes of commercial PWR nuclear power plants. When fission nuclides undergo fission reactions, most of the energy is released in a very short time after fission, which is called prompt power; while the other part of the energy is slowly released in the form of fission product decay, and its decay constant varies from 10 0 to 10 -14 The average time scale is about 5 minutes, and its total amount accounts for about 5% of the total fission energy, which is called decay power.

[0003] In existing PWR core physics analysis and calculations, it is generally assumed that the decay power is released directly and instantly at the moment of the fission reaction. In traditional core calculations, the time or burnup step is generally several hours, a day or even a few days. The time interval is long, and the release of decay power has tended to balance. The error caused by the above assumption can be ignored. However, the power of new reactors changes faster and more frequently over time, and the time step calculated by the core analysis software is also smaller. The error caused by the above assumption is no longer acceptable. 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 core power of a pressurized water reactor with a slow release of decay power, improve the accuracy of the power calculation of the two-step program, and ensure the consistency between the calculated core power and the actual core power in a small time step.

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

[0006] A method for calculating the delayed release of core decay power of a pressurized water reactor comprises the following steps:

[0007] Step 1: The two-dimensional grid calculation program Bamboo-Lattice uses a special decay heat release database to separately consider the energy release of fission product decay when calculating the energy release cross section; only the energy released promptly, the energy of the incident neutron, and the energy released by the radiation capture reaction are retained in the energy release cross section, which is specifically expressed as:

[0008] κ′ i =W fiss,i +W n,i Formula (1)

[0009]

[0010] Where:

[0011] κ′ i —— indicates the energy release of nuclide i without the heat of capture;

[0012] W fiss,i ——Indicates the prompt energy released by the fission of nuclide i;

[0013] W n,i ——represents the average incident neutron energy of nuclide i;

[0014] N i ——represents the nuclear density of nuclide i;

[0015] σ f,i,g ——represents the microscopic fission cross section of the gth group of nuclide i;

[0016] σ c,i,g ——represents the microscopic capture cross section of the gth group of nuclide i;

[0017] q i ——Indicates the energy released by each radiation capture of nuclide i;

[0018] κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products;

[0019] p i ——represents the energy released by each fission decay of nuclide i;

[0020] Step 2: The two-dimensional grid calculation program Bamboo-Lattice passes the calculated minority group parameters including the energy release cross section to the three-dimensional steady-state core calculation program Bamboo-Core. After solving the neutron diffusion equation, the three-dimensional steady-state core calculation program Bamboo-Core will obtain the neutron flux distribution shape of the core; the delayed release function of the decay power of each fission nuclide is calculated from the decay heat release database, which is expressed as:

[0021]

[0022] Where:

[0023] α i,g,j ——represents the fission yield of the jth decay heat precursor nucleus in the gth group of the fission system of nuclide i;

[0024] λ i,g,j ——denotes the decay constant of the jth decay heat precursor nucleus in the gth group of the fission system of nuclide i;

[0025] t——indicates the decay time;

[0026] When the PWR core is running, the nuclide fission reaction rate between two burnup points of a certain block is expressed as:

[0027] R f,i,l,g (t) = a i,k,l,g t+b i,k,l,g ,T k-1 <t≤T k Formula (4)

[0028] Where:

[0029] R f,i,l,g (t)——represents the fission reaction rate of the g-th group of nuclides i in node l at time t;

[0030] a i,k,l,g ——represents the first fission reaction rate coefficient of the g-th group of nuclides i in node l between the k-1th and kth burnup points;

[0031] b i,k,l,g ——represents the second fission reaction rate coefficient of the g-th group of nuclides i in node l between the k-1th and kth burnup points;

[0032] T k-1 , T k ——Indicates the time between the kth burnup point and the k-1th burnup point;

[0033] Step 3: From step 2, the delayed release function of the decay power of the fissile nuclides in each burnup section in the power history of the PWR core can be obtained. Based on this, the delayed release calculation equation of the decay power for each section of the PWR core is established on a time scale, which is expressed as:

[0034]

[0035] Where:

[0036] P d,l ——represents the decay power of node l;

[0037] f i,g ——represents the decay power release function of the g-th group of nuclide i;

[0038] R f,i,l,g (t)——represents the fission reaction rate of the g-th group of nuclides i in node l at time t;

[0039] n——represents the total number of burnup points counted;

[0040] m′——represents the total number of fissile nuclides counted;

[0041] G——indicates the number of energy groups counted in total;

[0042] Step 4: The core power equation is expressed as:

[0043]

[0044] Where:

[0045] P th ——Indicates the core thermal power;

[0046] C P ——represents the normalization factor;

[0047] κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products;

[0048] V l ——represents the volume of node l;

[0049] P d,l ——represents the decay power of node l;

[0050] L——indicates the total number of nodes counted;

[0051] Solve the normalization factor C by combining the decay power delayed release calculation equation with the core power equation P :

[0052]

[0053] Where:

[0054] P th ——Indicates the core thermal power;

[0055] C P ——represents the normalization factor;

[0056] κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products;

[0057] V l ——represents the volume of node l;

[0058] φ l,g ——indicates the three-dimensional neutron flux density distribution shape of the core of the g-th group of nodes l;

[0059] P d,l ——represents the decay power of node l;

[0060] f i,g ——represents the decay power release function of the g-th group of nuclide i;

[0061] R f,i,l,g ——represents the fission reaction rate of the g-th group of nuclides i in node l;

[0062] Step 5: Use the normalization factor C obtained in step 4 P , calculate the real power density distribution and relative power density distribution of the core, expressed as:

[0063]

[0064] Where:

[0065] ——Indicates the real power density of node l;

[0066] ——Indicates the relative power density of node l;

[0067] C P ——represents the normalization factor;

[0068] κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products; V l ——represents the volume of node l;

[0069] φ l,g ——indicates the three-dimensional neutron flux density distribution shape of the core of the g-th group of nodes l;

[0070] V l ——represents the volume of node l;

[0071] P d,l ——represents the decay power of node l;

[0072] V core ——Indicates the volume of the core active area.

[0073] Compared with the prior art, the present invention has the following advantages: when the core state changes rapidly in a short period of time, and the scale of the change time is in the order of minutes, the error caused by the calculation of power and neutron flux distribution by the decay power instantaneous release model is avoided, and in this scenario, the change of core neutron flux and power distribution in the actual core is better reflected. The present invention aims to realize the slow release calculation of decay power in the two-step pressurized water reactor core program, break through the limitations of the existing power calculation strategy, broaden the applicable scenarios of the existing core calculation software, and solve the problem that the power calculation strategy of the current pressurized water reactor core program is not suitable for new working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 This is the AP1000 local power reduction history.

[0075] Figure 2 is the AP1000 local core average neutron flux density history. DETAILED DESCRIPTION

[0076] The present invention is further described in detail below in conjunction with specific embodiments:

[0077] A method for calculating core power of a pressurized water reactor with slow decay power release comprises the following steps:

[0078] Step 1: The two-dimensional grid calculation program Bamboo-Lattice uses a special decay heat release database to separately consider the energy release of fission product decay when calculating the energy release cross section; only the prompt release energy, the energy of the incident neutron, and the energy release caused by the radiation capture reaction are retained in the energy release cross section, which is specifically expressed as:

[0079] κ′ i =W fiss,i +W n,i Formula (1)

[0080]

[0081] Where:

[0082] κ′ i —— indicates the energy release of nuclide i without the heat of capture;

[0083] W fiss,i ——Indicates the prompt energy released by the fission of nuclide i;

[0084] W n,i ——represents the average incident neutron energy of nuclide i;

[0085] N i ——represents the nuclear density of nuclide i;

[0086] σ f,i,g ——represents the microscopic fission cross section of the gth group of nuclide i;

[0087] σ c,i,g ——represents the microscopic capture cross section of the gth group of nuclide i;

[0088] q i ——Indicates the energy released by each radiation capture of nuclide i;

[0089] κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products;

[0090] p i ——represents the energy released by each fission decay of nuclide i;

[0091] Step 2: The two-dimensional grid calculation program Bamboo-Lattice passes the calculated minority group parameters including the energy release cross section to the three-dimensional steady-state core calculation program Bamboo-Core. After solving the neutron diffusion equation, the three-dimensional steady-state core calculation program Bamboo-Core will obtain the neutron flux distribution shape of the core; the delayed release function of the decay power of each fission nuclide is calculated from the decay heat release database, which is expressed as:

[0092]

[0093] Where:

[0094] α i,g,j ——represents the fission yield of the jth decay heat precursor nucleus in the gth group of the fission system of nuclide i;

[0095] λ i,g,j ——denotes the decay constant of the jth decay heat precursor nucleus in the gth group of the fission system of nuclide i;

[0096] t——indicates the decay time;

[0097] When the PWR core is running, the nuclide fission reaction rate between two burnup points of a certain block is expressed as:

[0098] R f,i,l,g (t) = a i,k,l,g t+b i,k,l,g ,T k-1 <t≤T k Formula (4)

[0099] Where:

[0100] R f,i,l,g (t)——represents the fission reaction rate of the g-th group of nuclides i in node l at time t;

[0101] a i,k,l,g ——represents the first fission reaction rate coefficient of the g-th group of nuclides i in node l between the k-1th and kth burnup points;

[0102] b i,k,l,g ——represents the second fission reaction rate coefficient of the g-th group of nuclides i in node l between the k-1th and kth burnup points;

[0103] T k-1 , T k ——Indicates the time between the kth burnup point and the k-1th burnup point;

[0104] Step 3: From step 2, the delayed release function of the decay power of the fissile nuclides in each burnup section in the power history of the PWR core can be obtained. Based on this, the delayed release calculation equation of the decay power for each section of the PWR core is established on a time scale, which is expressed as:

[0105]

[0106] Where:

[0107] P d,l ——represents the decay power of node l;

[0108] f i,g ——represents the decay power release function of the g-th group of nuclide i;

[0109] R f,i,l,g (t)——represents the fission reaction rate of the g-th group of nuclides i in node l at time t;

[0110] n——represents the total number of burnup points counted;

[0111] m′——represents the total number of fissile nuclides counted;

[0112] G——indicates the number of energy groups counted in total;

[0113] Step 4: The core power equation is expressed as:

[0114]

[0115] Where:

[0116] P th ——Indicates the core thermal power;

[0117] C P ——represents the normalization factor;

[0118] κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products;

[0119] V l ——represents the volume of node l;

[0120] P d,l ——represents the decay power of node l;

[0121] L——indicates the total number of nodes counted;

[0122] Solve the normalization factor C by combining the decay power delayed release calculation equation with the core power equation P :

[0123]

[0124] Where:

[0125] P th ——Indicates the core thermal power;

[0126] C P ——represents the normalization factor;

[0127] κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products;

[0128] V l ——represents the volume of node l;

[0129] φ l,g ——indicates the three-dimensional neutron flux density distribution shape of the core of the g-th group of nodes l;

[0130] P d,l ——represents the decay power of node l;

[0131] f i,g ——represents the decay power release function of the g-th group of nuclide i;

[0132] R f,i,l,g ——represents the fission reaction rate of the g-th group of nuclides i in node l;

[0133] Step 5: Use the normalization factor C obtained in step 4 P , calculate the real power density distribution and relative power density distribution of the core, expressed as:

[0134]

[0135] Where:

[0136] ——Indicates the real power density of node l;

[0137] ——Indicates the relative power density of node l;

[0138] C P ——represents the normalization factor;

[0139] κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products; V l ——represents the volume of node l;

[0140] φ l,g ——indicates the three-dimensional neutron flux density distribution shape of the core of the g-th group of nodes l;

[0141] V l ——represents the volume of node l;

[0142] P d,l ——represents the decay power of node l;

[0143] V core ——Indicates the volume of the core active area.

[0144] The verification and results of the method of the present invention are as follows:

[0145] The verification background selected the first cycle of the AP1000 core, in which a power reduction history, such as Figure 1 The power reduction amplitude of this power history is that the core power is reduced from 48.24% to 15.96% in 10 minutes, which is suitable for the decay power slow release method. Therefore, the method of the present invention is verified in this context.

[0146] Respectively Figure 1 In the power history stage shown, a burnup point is selected before and after the power is reduced, and the relative power density distribution of the core is calculated using the decay power slow release method and the decay power instant release method in the prior art, as shown in Table 1 and Table 2. Table 1 and Table 2 are the relative power density distributions corresponding to the two burnup points before and after the power reduction, respectively, wherein the first part of the two tables represents the relative power density distribution of the core calculated by the decay power slow release method, the second part represents the relative power density distribution of the core calculated by the decay power instant release method, and the third part represents the relative deviation of the first two parts. It can be seen that there are three positions in the relative power density distribution of the burnup point after the power reduction relative to the burnup point before the power reduction, which are all the positions of the power regulation control rod.

[0147] Table 1 shows the relative power density distribution at a burnup point before core power reduction.

[0148]

[0149] Table 2 shows the relative power density distribution of a burnup point after core power reduction

[0150]

[0151] Due to the movement of the control rods, the neutron flux level of the corresponding components and the surrounding areas changes rapidly, and the prompt power changes rapidly; however, in the decay power slow release method, it takes time for the decay power to react to the neutron flux change. For the burnup point after power reduction, the average core neutron flux level calculated by the decay power slow release method is 4.6% higher than the average core flux level calculated by the decay power instant release method. Figure 2 shown.

[0152] Therefore, it is believed that the use of the decay power slow release method can better reflect the changes in the core neutron flux and power distribution in the actual core in the scenario of adjusting the core power in a short time than the existing decay power instantaneous release method.

Claims

1. A method for calculating core power of a pressurized water reactor with slow decay power release, characterized in that: The steps include: Step 1: The two-dimensional grid calculation program Bamboo-Lattice uses a special decay heat release database to separately consider the energy release of fission product decay when calculating the energy release cross section; only the energy released promptly, the energy of the incident neutron, and the energy released by the radiation capture reaction are retained in the energy release cross section, which is specifically expressed as: κ′ i =W fiss,i +W n,i Formula (1) Where: κ′ i —— indicates the energy release of nuclide i without the heat of capture; W fiss,i ——Indicates the prompt energy released by the fission of nuclide i; W n,i ——represents the average incident neutron energy of nuclide i; N i ——represents the nuclear density of nuclide i; σ f,i,g ——represents the microscopic fission cross section of the gth group of nuclide i; σ c,i,g ——represents the microscopic capture cross section of the gth group of nuclide i; q i ——Indicates the energy released by each radiation capture of nuclide i; κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products; p i ——represents the energy released by each fission decay of nuclide i; Step 2: The two-dimensional grid calculation program Bamboo-Lattice passes the calculated minority group parameters including the energy release cross section to the three-dimensional steady-state core calculation program Bamboo-Core. After solving the neutron diffusion equation, the three-dimensional steady-state core calculation program Bamboo-Core will obtain the neutron flux distribution shape of the core; the delayed release function of the decay power of each fission nuclide is calculated from the decay heat release database, which is expressed as: Where: α i,g,j ——represents the fission yield of the jth decay heat precursor nucleus in the gth group of the fission system of nuclide i; λ i,g,j ——denotes the decay constant of the jth decay heat precursor nucleus in the gth group of the fission system of nuclide i; t——indicates the decay time; When the PWR core is running, the nuclide fission reaction rate between two burnup points of a certain block is expressed as: R f,i,l,g (t) = a i,k,l,g t+b i,k,l,g ,T k-1 <t≤T k Formula (4) Where: R f,i,l,g (t)——represents the fission reaction rate of the g-th group of nuclides i in node l at time t; a i,k,l,g ——represents the first fission reaction rate coefficient of the g-th group of nuclides i in node l between the k-1th and kth burnup points; b i,k,l,g ——represents the second fission reaction rate coefficient of the g-th group of nuclides i in node l between the k-1th and kth burnup points; T k-1 、T k ——Indicates the time of the kth burnup point and the k-1th burnup point; Step 3: The delayed release function of the decay power of the fissile nuclides in each burnup section in the power history of the PWR core is obtained from step 2. Based on this, the delayed release calculation equation of the decay power of each section of the PWR core is established on a time scale, which is expressed as: Where: P d,l ——represents the decay power of node l; f i,g ——represents the decay power release function of the g-th group of nuclide i; R f,i,l,g (t)——represents the fission reaction rate of the g-th group of nuclides i in node l at time t; n——represents the total number of burnup points counted; m′——represents the total number of fissile nuclides counted; G——indicates the number of energy groups counted in total; Step 4: The core power equation is expressed as: Where: P th ——Indicates the core thermal power; C P ——represents the normalization factor; κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products; V l ——represents the volume of node l; P d,l ——represents the decay power of node l; L——indicates the total number of nodes counted; Solve the normalization factor C by combining the decay power delayed release calculation equation with the core power equation P : Where: P th ——Indicates the core thermal power; C P ——represents the normalization factor; κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products; V l ——represents the volume of node l; φ l,g ——indicates the three-dimensional neutron flux density distribution shape of the core of the g-th group of nodes l; V l ——represents the volume of node l; P d,l ——represents the decay power of node l; f i,g ——represents the decay power release function of the g-th group of nuclide i; R f,i,l,g ——represents the fission reaction rate of the g-th group of nuclides i in node l; Step 5: Use the normalization factor C obtained in step 4 P , calculate the real power density distribution and relative power density distribution of the core, expressed as: Where: ——Indicates the real power density of node l; ——Indicates the relative power density of node l; C P ——represents the normalization factor; κΣ′ f,m,g ——The macroscopic heat release cross section of the g-th group in region m does not include the heat release due to decay of fission products; V l ——represents the volume of node l; φ l,g ——indicates the three-dimensional neutron flux density distribution shape of the core of the g-th group of nodes l; V l ——represents the volume of node l; P d,l ——represents the decay power of node l; V core ——Indicates the volume of the core active area.

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