Method for determining Doppler reactivity of fuel of reactor

Abstract

The embodiment of the invention relates to the technical field of reactivity calculation of a nuclear reactor, in particular to a method for determining Doppler reactivity of fuel of a reactor, which comprises the following steps: determining a Doppler constant; obtaining steady-state fuel components, steady-state fuel mass and steady-state fuel temperature of the reactor; determining the initial Doppler reactivity of the reactor according to the Doppler constant, the steady-state fuel component, the steady-state fuel mass and the steady-state fuel temperature; updating the Doppler reactivity of the reactor according to the transient fuel component, the transient fuel mass and the transient fuel temperature of the reactor; and determining the transient Doppler reactivity according to the initial Doppler reactivity and the updated Doppler reactivity. According to the method provided by the embodiment of the invention, the change of Doppler reactivity along with time in the transient process can be calculated, the precision is relatively high, the reactivity feedback calculation capability in the initial stage of fuel melting can be improved, and the analysis requirement on serious accidents of the sodium-cooled fast neutron nuclear reactor can be met.

Description

Technical Field

[0001] Embodiments of the present application relate to the technical field of nuclear reactor reactivity calculation, and in particular to a method for determining the Doppler reactivity of reactor fuel. Background Art

[0002] The statements herein merely provide background information related to the present application and do not necessarily constitute prior art.

[0003] A sodium-cooled fast neutron reactor (SFR) uses liquid sodium as a coolant and is capable of generating fission reactions using high-energy fast neutrons. In SFR accident analysis, a point-reactor model is typically used to calculate neutron dynamics, and various reactivity changes are calculated using a lumped parameter approach.

[0004] However, when the fuel temperature rises, the thermal motion of the fuel atoms will intensify, causing the velocity distribution of the nuclides interacting with neutrons to become wider, even the resonance peak to broaden, thereby producing a fuel Doppler effect and causing changes in the fuel reactivity. Traditional methods for calculating transient fuel reactivity changes have many shortcomings. Summary of the Invention

[0005] A brief overview of the present application is provided below to provide a basic understanding of certain aspects of the present application. It should be understood that this overview is not an exhaustive overview of the present application. It is not intended to identify key or important portions of the present application, nor is it intended to limit the scope of the present application. Its purpose is simply to present certain concepts in a simplified form as a prelude to the more detailed description that will be discussed later.

[0006] An embodiment of the present application provides a method for determining the Doppler reactivity of a reactor fuel, which includes the following steps: S1, determining a Doppler constant based on a change in Doppler reactivity due to a temperature change of the fuel; S2, obtaining a steady-state fuel composition, a steady-state fuel mass, and a steady-state fuel temperature of the reactor; S3, determining an initial Doppler reactivity of the reactor based on the Doppler constant determined in step S1 and the steady-state fuel composition, the steady-state fuel mass, and the steady-state fuel temperature obtained in step S2; S4, updating the Doppler reactivity of the reactor at any transient moment based on the transient fuel composition, the transient fuel mass, and the transient fuel temperature of the reactor; S5, determining a transient Doppler reactivity within the transient moment based on the initial Doppler reactivity determined in step S3 and the updated Doppler reactivity determined in step S4.

[0007] The method provided in the embodiments of the present application determines the transient Doppler reactivity of the reactor at a transient moment based on the initial Doppler reactivity of the reactor and the updated Doppler reactivity at any transient moment. It can calculate the change of Doppler reactivity over time in the transient process with high accuracy, which is conducive to improving the reactivity feedback calculation capability of the initial stage of fuel melting, thereby meeting the analysis requirements of serious accidents of sodium-cooled fast neutron nuclear reactors.

[0008] These and other advantages of the present application will become more apparent through the following detailed description of the preferred embodiments of the present application in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] To further illustrate the above and other advantages and features of the present application, the following detailed description of specific embodiments of the present application is provided in conjunction with the accompanying drawings. The accompanying drawings, together with the detailed description below, are incorporated into and form a part of this specification. Elements with the same function and structure are denoted by the same reference numerals. It should be understood that these drawings depict only typical examples of the present application and should not be construed as limiting the scope of the present application.

[0010] Figure 1 is a schematic flow chart of a method for determining the Doppler reactivity of fuel of a reactor according to an embodiment of the present application.

[0011] It should be noted that the drawings are not necessarily drawn to scale, but are merely shown in a schematic manner that does not affect the reader's understanding. DETAILED DESCRIPTION

[0012] Exemplary embodiments of the present application will be described below with reference to the accompanying drawings. For the sake of clarity and conciseness, not all features of actual implementations are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the process of developing any such actual implementation in order to achieve the developer's specific goals, such as meeting those constraints related to the system and business, and these constraints may vary depending on the implementation. In addition, it should be understood that although the development work may be very complex and time-consuming, it is a routine task for those skilled in the art who benefit from the content of this application.

[0013] It is also necessary to explain here that, in order to avoid obscuring the present application due to unnecessary details, the accompanying drawings only show the device structure and / or processing steps that are closely related to the solution according to the present application, while other details that are not closely related to the present application are omitted.

[0014] It should be noted that, unless otherwise defined, the technical or scientific terms used in this application should have the common meanings understood by persons having ordinary skills in the field to which this application belongs.

[0015] In the description of the embodiments of the present application, “multiple” means at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0016] Traditional methods for calculating reactivity usually calculate the fuel Doppler reactivity based on changes in the average temperature of the reactor fuel. This calculation method is suitable for scenarios where the fuel temperature distribution remains unchanged and the fuel morphology is fixed. However, in the early stages of a serious accident in a sodium-cooled fast neutron nuclear reactor, the fuel morphology will change and move, making traditional methods for calculating transient fuel Doppler reactivity inapplicable.

[0017] In order to solve the above technical problems, an embodiment of the present application provides a method for determining the Doppler reactivity of the fuel of a reactor. Figure 1 is a schematic flow chart of a method for determining the Doppler reactivity of a reactor fuel according to an embodiment of the present application, such as Figure 1 As shown, the determination method includes the following steps S1 to S5.

[0018] S1. Determine the Doppler constant based on the change in Doppler reactivity due to the temperature change of the fuel.

[0019] S2. Obtain the steady-state fuel composition, steady-state fuel mass, and steady-state fuel temperature of the reactor.

[0020] S3. Determine the initial Doppler reactivity of the reactor based on the Doppler constant determined in step S1 and the steady-state fuel composition, steady-state fuel mass, and steady-state fuel temperature obtained in step S2.

[0021] S4. At any transient moment, the Doppler reactivity of the reactor is updated according to the transient fuel composition, transient fuel mass, and transient fuel temperature of the reactor.

[0022] S5. Determine the transient Doppler reactivity within the transient moment according to the initial Doppler reactivity determined in step S3 and the updated Doppler reactivity determined in step S4.

[0023] The method provided in the embodiments of the present application determines the transient Doppler reactivity of the reactor at a transient moment based on the initial Doppler reactivity of the reactor and the updated Doppler reactivity at any transient moment. It can calculate the change of Doppler reactivity over time in the transient process with high accuracy, which is conducive to improving the reactivity feedback calculation capability of the initial stage of fuel melting, thereby meeting the analysis requirements of serious accidents of sodium-cooled fast neutron nuclear reactors.

[0024] In some embodiments, in step S1, a three-dimensional fuel Doppler constant distribution is determined based on perturbation theory, and then a Doppler reactivity change due to a temperature change of the fuel is determined based on the three-dimensional fuel Doppler constant distribution.

[0025] In some embodiments, the Doppler constant satisfies the following expression (1):

[0026] α fD (i,j,k)=T f (i,j,k)(dρ / dT) / m fuel (i,j,k)(1).

[0027] Among them, α fD (i, j, k) represents the Doppler constant within the grid; T f (i, j, k) represents the fuel temperature within the grid; ρ represents the Doppler reactivity change due to the fuel temperature change within the grid; T represents the fuel temperature; m fuel (i, j, k) represents the fuel mass within the grid.

[0028] The method provided in the embodiment of the present application determines the Doppler constant through the above expression (1), with high accuracy and reliability.

[0029] In some embodiments, before step S3, the method further includes: dividing the reactor into grids to obtain a plurality of grids; wherein, in step S3, the initial Doppler reactivity of the reactor includes the initial Doppler reactivity of the corresponding grids in each grid in the reactor.

[0030] The method provided in the embodiment of the present application divides the reactor into grids to obtain multiple grids, and then determines the grid initial Doppler reactivity corresponding to each grid, which is conducive to ensuring the accuracy of the determined grid initial Doppler reactivity.

[0031] In some embodiments, step S4 includes: S41. At any transient moment, updating the Doppler reactivity of each grid according to the transient fuel composition, transient fuel mass and transient fuel temperature in each grid of the reactor; S42. Determining the updated Doppler reactivity of the reactor according to the updated Doppler reactivity of each grid.

[0032] The method provided in the embodiment of the present application updates the Doppler reactivity of the grid at any transient moment, and then determines the updated Doppler reactivity of the reactor based on the updated Doppler reactivity of each grid, thereby further ensuring the accuracy of the updated Doppler reactivity of the reactor.

[0033] In some embodiments, in step S3, at the steady-state moment, the initial Doppler reactivity satisfies the following expression (2):

[0034] Δρ Doppler,t0 (i,j,k)=m fuel,S,t0 (i,j,k)α fD (i,j,k)ln(T f,S,t0 (i,j,k) / T0)+m fuel,L,t0 (i,j,k)α fD (i,j,k)ln(T f,L,t0 (i,j,k) / T0) (2).

[0035] Where (i, j, k) represents the position of any grid in the reactor; Δρ Doppler,t0 (i, j, k) represents the Doppler reactivity change in the grid due to the temperature change of the fuel at the steady state moment; m fuel,S,t0 (i, j, k) represents the steady-state solid fuel mass in the grid at the steady-state moment; m fuel,L,t0 (i, j, k) represents the steady-state liquid fuel mass in the grid at the steady-state moment, which includes the steady-state solid fuel mass and the steady-state liquid fuel mass; α fD (i, j, k) represents the Doppler constant in the grid; T0 represents the steady-state temperature; T f,S,t0 (i, j, k) represents the steady-state solid fuel temperature in the grid at the steady-state moment; T f,L,t0 (i, j, k) represents the steady-state liquid fuel temperature in the grid at the steady-state moment, where the steady-state fuel temperature includes the steady-state solid fuel temperature and the steady-state liquid fuel temperature.

[0036] The method provided in the embodiment of the present application determines the initial Doppler reactivity at the steady state moment through the above expression (2), which is highly efficient.

[0037] In some embodiments, when the fuel is not melted, the steady-state liquid fuel mass is zero. However, since the steady-state liquid fuel temperature in the above expression (2) cannot be zero, the steady-state solid fuel temperature can be assigned to the steady-state liquid fuel temperature without affecting the final calculation result.

[0038] In some embodiments, the steady-state temperature T0 can be any positive value, and the values ​​corresponding to the steady-state temperature T0 in all grids are the same to avoid sudden changes in calculation results when the fuel moves.

[0039] In such an embodiment, the steady-state temperature T0 may be the average temperature of the fuel at the steady-state moment.

[0040] In some embodiments, in step S4, the updated Doppler reactivity satisfies the following expression (3):

[0041] Δρ Doppler,t (i,j,k)=m fuel,S,t (i,j,k)α fD (i,j,k)ln(T f,S,t (i,j,k) / T0)+m fuel,L,t (i,j,k)α fD (i,j,k)ln(T f,L,t (i,j,k) / T0) (3).

[0042] Where (i, j, k) represents the position of any grid in the reactor; Δρ Doppler,t (i, j, k) represents the Doppler reactivity change in the grid due to the temperature change of the fuel at the transient moment; m fuel,S,t (i, j, k) represents the transient solid fuel mass in the grid at the transient moment; m fuel,L,t (i, j, k) represents the transient liquid fuel mass in the grid at the transient moment, which includes the transient solid fuel mass and the transient liquid fuel mass; α fD (i, j, k) represents the Doppler constant in the grid; T0 represents the steady-state temperature; T f,S,t (i, j, k) represents the transient solid fuel temperature in the grid at the transient moment; T f,L,t (i, j, k) represents the transient liquid fuel temperature in the grid at the transient moment, and the transient fuel temperature includes the transient solid fuel temperature and the transient liquid fuel temperature.

[0043] The method provided in the embodiment of the present application updates the initial Doppler reactivity at the steady-state moment through the above expression (3), thereby ensuring the accuracy of the updated Doppler reactivity.

[0044] In some embodiments, in step S5, the transient Doppler reactivity satisfies the following expression (4):

[0045]

[0046] Where (i, j, k) represents the position of any grid in the reactor; Δρ Doppler (t) represents the transient Doppler reactivity; t represents the transient time; Δρ Doppler,t (i, j, k) represents the Doppler reactivity change in the grid due to the temperature change of the fuel at the transient moment; Δρ Doppler,t0 (i, j, k) represents the Doppler reactivity change within the grid due to the temperature change of the fuel at a steady state moment.

[0047] The method provided in the embodiment of the present application determines the transient Doppler reactivity of the reactor through the above expression (4), which is conducive to ensuring the reliability of the obtained Doppler reactivity change of the reactor within the transient moment.

[0048] In some embodiments, in step S1, the change in Doppler reactivity due to the temperature change of the fuel satisfies the following expression (5):

[0049]

[0050] Among them, P g represents the reactivity introduced by the gth group per unit volume; represents the conjugate neutron flux density of the gth group; δ represents the change; D g represents the diffusion coefficient of the gth group; φ g represents the neutron flux density of the gth group; g represents the neutron energy group number; r represents removal from this group; g' represents the number of other groups except this group; s represents scattering; k represents the effective multiplication factor; χ g represents the neutron production spectrum of the gth group; φ g' represents the conjugate neutron flux density of the gth group; represents the change in Doppler reactivity due to temperature change of the fuel; G represents the total number of neutron energy groups; v represents the number of neutrons produced in each fission; f represents the fission reaction; and V represents the volume of the calculation unit.

[0051] The method provided in the embodiment of the present application determines the Doppler reactivity change caused by the temperature change of the fuel through the above expression (5), and can determine the Doppler reactivity change with spatial distribution when the fuel undergoes morphological changes and movement behavior.

[0052] In some embodiments, according to perturbation theory, the above expression (5) can be derived from the multi-group diffusion equation. Expression (5) is used to reflect the conservation relationship of the total value of neutrons in the steady state. Through expression (5), the reactivity contribution of any position in the three-dimensional space can be determined. It is mainly composed of leakage effect (diffusion coefficient perturbation), absorption effect (removal cross section perturbation), moderation effect (scattering matrix perturbation), and fission effect (fission cross section perturbation). After the temperature of the fuel changes, the perturbation amount of diffusion coefficient perturbation, removal cross section perturbation, scattering matrix perturbation, and fission cross section perturbation can be obtained through Doppler resonance processing. Then, the reactivity contribution at any position in the three-dimensional space is determined, and the reactivity contribution at each position in the entire space is volume integrated to determine the lumped reactivity change.

[0053] In some embodiments, the transient Doppler reactivity of the reactor may be determined by summing the transient Doppler reactivity within each grid.

[0054] In such an embodiment, the transient Doppler reactivity of the reactor satisfies the following expression (6):

[0055] ρ(t)=ρ e (t)+ρ fb,other (t)+Δρ Doppler (t) (6).

[0056] Where ρ(t) represents the total reactivity of the reactor; t represents the transient time; ρ fb,other (t) represents other reactivity except Doppler reactivity; ρ e (t) represents the external reactivity of the reactor; Δρ Doppler (t) represents the transient Doppler reactivity of the reactor.

[0057] In some embodiments, the point pile neutron kinetic equations satisfy the following expressions (7) and (8):

[0058]

[0059] Where N(t) represents the fission power of the reactor core; t represents the transient time; ρ(t) represents the total reactivity of the reactor; β represents the effective delayed neutron fraction; Λ represents the neutron generation time; λ i represents the time constant of the i-th group of delayed neutron decay; C i (t) represents the concentration of delayed neutron precursor nuclei in group i; β i represents the delayed neutron fraction of group i.

[0060] In some embodiments, the power change of the reactor is determined by substituting the total reactivity ρ(t) of the reactor into the point reactor neutron kinetic equations of expressions (7) and (8) above.

[0061] In some embodiments, thermal-hydraulic calculations are re-performed based on the power change of the determined reactor to determine the transient fuel composition, transient fuel mass and transient fuel temperature of the reactor at the next transient moment, and steps S3 to S5 in the embodiments of the present application are repeated to determine the transient Doppler reactivity of the reactor at the next transient moment.

[0062] In some embodiments, after step S5, the method further includes: correcting the transient Doppler reactivity to ensure the accuracy of the determined transient Doppler reactivity.

[0063] In some embodiments, since the sodium boiling effect has a significant impact on the Doppler reactivity, the Doppler reactivity under the sodium boiling condition may be corrected to improve the accuracy of the transient Doppler reactivity.

[0064] In some embodiments, the corrected transient Doppler reactivity satisfies the following expression (9):

[0065]

[0066] Where Δρ' Doppler (t) represents the corrected transient Doppler reactivity; a1 represents the Doppler constant of the non-space-time reactor; a2 represents the Doppler constant of the full-space-time reactor; α Void,t represents the sodium cavitation fraction in the reactor at the transient moment; Δρ Doppler (t) represents the transient Doppler reactivity before correction.

[0067] The method provided in the embodiment of the present application uses the above expression (9) to correct the determined transient Doppler reactivity to further improve the accuracy of the obtained transient Doppler reactivity.

[0068] In such an embodiment, the effect of coolant cavitation on neutron leakage is corrected by linearly adjusting the input Doppler constants for the non-cavitation and cavitation times.

[0069] Regarding the embodiments of the present application, it should also be noted that, in the absence of conflict, the embodiments of the present application and the features therein can be combined with each other to obtain new embodiments.

[0070] The above description is only a specific implementation method of the present application, but the protection scope of the present application is not limited thereto. The protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for determining the Doppler reactivity of a fuel of a reactor, characterized in that It includes the following steps: S1. determining a Doppler constant according to a change in Doppler reactivity caused by a temperature change of the fuel; S2. Obtaining a steady-state fuel component, a steady-state fuel mass and a steady-state fuel temperature of the fuel; S3, determining the initial Doppler reactivity of the reactor according to the Doppler constant determined in step S1, and the steady-state fuel composition, the steady-state fuel mass and the steady-state fuel temperature obtained in step S2; S4. At any transient moment, updating the Doppler reactivity of the reactor according to the transient fuel composition, transient fuel mass and transient fuel temperature of the reactor; S5. Determine the transient Doppler reactivity within the transient moment according to the initial Doppler reactivity determined in step S3 and the updated Doppler reactivity determined in step S4.

2. The method according to claim 1, characterized in that Before step S3, the method further includes: dividing the reactor into grids to obtain a plurality of grids; Wherein, in step S3, the initial Doppler reactivity of the reactor includes the initial Doppler reactivity of the corresponding grid in each grid in the reactor.

3. The method according to claim 2, characterized in that The S4 step includes: S41, at any transient moment, updating the Doppler reactivity of each grid according to the transient fuel composition, the transient fuel mass and the transient fuel temperature in each grid of the reactor; S42. Determine the updated Doppler reactivity of the reactor according to the updated Doppler reactivity of each grid.

4. The method according to claim 3, characterized in that In step S3, at the steady state, the initial Doppler responsiveness satisfies the following expression: Δρ Doppler,t0 (i,j,k)=m fuel,S,t0 (i,j,k)α fD (i,j,k)ln(T f,S,t0 (i,j,k) / T0)+m fuel,L,t0 (i,j,k)α fD (i,j,k)ln(T f,L,t0 (i,j,k) / T0); Where (i, j, k) represents the position of any grid in the reactor; Δρ Doppler,t0 (i, j, k) represents the Doppler reactivity change in the grid due to the temperature change of the fuel at a steady state moment; m fuel,S,t0 (i, j, k) represents the steady-state solid fuel mass in the grid at the steady-state moment; m fuel,L,t0 (i, j, k) represents the steady-state liquid fuel mass in the grid at the steady-state moment, and the steady-state fuel mass includes the steady-state solid fuel mass and the steady-state liquid fuel mass; α fD (i, j, k) represents the Doppler constant in the grid; T0 represents the steady-state temperature; T f,S,t0 (i, j, k) represents the steady-state solid fuel temperature in the grid at the steady-state moment; T f,L,t0 (i, j, k) represents the steady-state liquid fuel temperature in the grid at the steady-state moment, and the steady-state fuel temperature includes the steady-state solid fuel temperature and the steady-state liquid fuel temperature.

5. The method according to claim 4, characterized in that In step S4, the updated Doppler responsiveness satisfies the following expression: Δρ Doppler,t (i,j,k)=m fuel,S,t (i,j,k)α fD (i,j,k)ln(T f,S,t (i,j,k) / T0)+m fuel,L,t (i,j,k)α fD (i,j,k)ln(T f,L,t (i,j,k) / T0); Where (i, j, k) represents the position of any grid in the reactor; Δρ Doppler,t (i, j, k) represents the Doppler reactivity change in the grid due to the temperature change of the fuel at the transient moment; m fuel,S,t (i, j, k) represents the transient solid fuel mass in the grid at the transient moment; m fuel,L,t (i, j, k) represents the transient liquid fuel mass in the grid at the transient moment, wherein the transient fuel mass includes the transient solid fuel mass and the transient liquid fuel mass; α fD (i, j, k) represents the Doppler constant in the grid; T0 represents the steady-state temperature; T f,S,t (i, j, k) represents the transient solid fuel temperature in the grid at the transient moment; T f,L,t (i, j, k) represents the transient liquid fuel temperature in the grid at the transient moment, and the transient fuel temperature includes the transient solid fuel temperature and the transient liquid fuel temperature.

6. The method according to claim 5, characterized in that In step S5, the transient Doppler responsiveness satisfies the following expression: Where (i, j, k) represents the position of any grid in the reactor; Δρ Doppler (t) represents the transient Doppler reactivity; t represents the transient time; Δρ Doppler,t (i, j, k) represents the Doppler reactivity change in the grid due to the temperature change of the fuel at the transient moment; Δρ Doppler,t0 (i, j, k) represents the Doppler reactivity change in the grid due to the temperature change of the fuel at a steady state moment.

7. The method according to claim 2, characterized in that: In step S1, the change in Doppler reactivity due to the temperature change of the fuel satisfies the following expression: Among them, P g represents the reactivity introduced by the gth group per unit volume; represents the conjugate neutron flux density of the g-th group; δ represents the change; D g represents the diffusion coefficient of the g-th group; φ g represents the neutron flux density of the g-th group; g represents the neutron energy group number; r represents removal from the group; g' represents the number of other groups except the group; s represents scattering; k represents the effective proliferation factor; χ g represents the neutron production spectrum of the g-th group; φ g' represents the conjugate neutron flux density of the g-th group; represents the change in Doppler reactivity due to the temperature change of the fuel; G represents the total number of neutron energy groups; v represents the number of neutrons produced in each fission; f represents the fission reaction; and V represents the volume of the calculation unit.

8. The method according to claim 7, characterized in that The Doppler constant satisfies the following expression: α fD (i,j,k)=T f (i,j,k)(dρ / dT) / m fuel (i,j,k); Among them, α fD (i, j, k) represents the Doppler constant in the grid; T f (i, j, k) represents the fuel temperature in the grid; ρ represents the Doppler reactivity change caused by the fuel temperature change in the grid; T represents the fuel temperature; m fuel (i, j, k) represents the fuel mass within the grid.

9. The method according to any one of claims 1 to 8, characterized in that: After the step S5, the method further includes: A correction is made for the transient Doppler reactivity.

10. The method according to claim 9, characterized in that The modified transient Doppler responsiveness satisfies the following expression: Among them, Δρ' Doppler (t) represents the modified transient Doppler reactivity; a1 represents the Doppler constant of the reactor when it is not empty; a2 represents the Doppler constant of the reactor when it is completely empty; α Void,t represents the sodium cavitation fraction in the reactor at the transient moment; Δρ Doppler (t) represents the transient Doppler reactivity before correction.

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