Method of determining doppler reactivity of fuel of a reactor

Abstract

Embodiments of the present application relate to the technical field of reactivity calculation of nuclear reactors, and particularly relate to a method for determining Doppler reactivity of fuel of a reactor, comprising: determining a Doppler constant; obtaining steady-state fuel composition, steady-state fuel mass and steady-state fuel temperature of the reactor; determining initial Doppler reactivity of the reactor according to the Doppler constant and the steady-state fuel composition, the steady-state fuel mass and the steady-state fuel temperature; updating Doppler reactivity of the reactor according to transient fuel composition, transient fuel mass and transient fuel temperature of the reactor; and determining transient Doppler reactivity according to the initial Doppler reactivity and the updated Doppler reactivity. The method provided by the embodiments of the present application can realize calculation of changes of Doppler reactivity over time in a transient process, has high precision, is beneficial to improving reactivity feedback calculation capability in the initial stage of fuel melting, and meets the analysis requirement for severe accidents of sodium-cooled fast neutron nuclear reactors.

Description

TECHNICAL FIELD

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

[0002] The statements herein are merely provided to give a basic understanding of some aspects of the present application, and are not necessarily intended to constitute the prior art.

[0003] A sodium-cooled fast neutron nuclear reactor is a fast neutron reactor using liquid sodium as a coolant, which can utilize high-energy fast neutrons for fission reactions. In the accident analysis of the sodium-cooled fast neutron nuclear reactor, a point reactor model is usually used to calculate the neutron kinetics, and a lumped parameter method is used to calculate various types of reactivity changes.

[0004] However, when the fuel temperature rises, the thermal motion of the fuel atoms will intensify, resulting in a broadening of the velocity distribution of the nuclides interacting with neutrons, even the resonance peak broadens, thereby producing a fuel Doppler effect, causing changes in fuel reactivity, and the traditional method of calculating transient fuel reactivity changes has many deficiencies. SUMMARY

[0005] A brief summary of the present application is given in the following to provide a basic understanding of some aspects of the present application. It should be understood that this summary is not an exhaustive overview of the present application. It is not intended to identify key or important parts of the present application nor is it intended to limit the scope of the present application. Its purpose is merely to present some concepts in a simplified form as a prelude to the more detailed description that is discussed later.

[0006] Embodiments of the present application provide a method for determining Doppler reactivity of fuel of a reactor, comprising the following steps: S1, determining a Doppler constant according to Doppler reactivity changes due to temperature changes of the fuel; S2, obtaining steady-state fuel composition, steady-state fuel mass and steady-state fuel temperature of the reactor; S3, determining initial Doppler reactivity of the reactor according to the Doppler constant determined in the S1 step and the steady-state fuel composition, the steady-state fuel mass and the steady-state fuel temperature obtained in the S2 step; S4, updating the Doppler reactivity of the reactor according to the transient fuel composition, the transient fuel mass and the transient fuel temperature of the reactor at any transient moment; S5, determining the transient Doppler reactivity at the transient moment according to the initial Doppler reactivity determined in the S3 step and the updated Doppler reactivity determined in the S4 step.

[0007] The method provided by the embodiment of the present application determines the transient Doppler reactivity of the reactor at the transient moment according to the initial Doppler reactivity of the reactor and the updated Doppler reactivity at any transient moment, can realize the calculation of the change of the Doppler reactivity with time in the transient process, has high accuracy, is beneficial to improving the reactivity feedback calculation capability at the initial fuel melting stage, and thus meets the analysis requirement of the severe accident of the sodium-cooled fast neutron nuclear reactor.

[0008] These and other advantages of the present application will no doubt become obvious to those of ordinary skill in the art after a reading of the following detailed description of the preferred embodiments when taken with the drawings. BRIEF DESCRIPTION OF DRAWINGS

[0009] In order to further illustrate the above and other advantages and features of the present application, a specific embodiment of the present application will be described in further detail below with reference to the accompanying drawings. The accompanying drawings form a part of the specification. Elements that have the same function and structure are denoted by the same reference signs. It should be understood that these drawings are only intended to describe typical examples of the present application and should not be regarded 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 the 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 intended to show the schematic manner in which the embodiments of the present application are implemented. DETAILED DESCRIPTION

[0012] In the following, exemplary embodiments of the present application will be described with reference to the accompanying drawings. In the specification, not all the features of the actual embodiments are described for the sake of clarity and conciseness. However, it should be appreciated that many implementation-specific decisions can have to be made in order to develop any such actual embodiment, to achieve the specific goals, such as compliance with system- and business-related constraints, which will vary from one implementation to another. Moreover, it should be appreciated that, while the development work can be very complex and time-consuming, such development work would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure.

[0013] It should also be noted that, in order to avoid obscuring the present application with unnecessary details, only the device structures and / or processing steps closely related to the scheme according to the present application are shown in the drawings, and other details not closely related to the present application are omitted.

[0014] It should be noted that the technical terms or scientific terms used in the description of the embodiments of the present application shall have the usual meaning understood by a person with ordinary skills in the art to which the present application pertains, unless otherwise defined.

[0015] In the description of the embodiments of the present application, the meaning of "a plurality of" is at least two, for example, two, three, etc., unless otherwise explicitly and specifically limited.

[0016] For the conventional method of calculating reactivity, it is usually based on the change of the average temperature of the fuel of the reactor to calculate the fuel Doppler reactivity, and such a calculation method is applicable to the scenario where the fuel temperature distribution is unchanged and the fuel form is fixed. However, in the initial stage of a severe accident of a sodium-cooled fast neutron nuclear reactor, the form of the fuel will change and a moving behavior will be generated, and the conventional method of calculating transient fuel Doppler reactivity is not applicable.

[0017] In view of the above technical problems, the embodiments of the present application provide a method for determining the Doppler reactivity of the fuel of a reactor, Figure 1 is a schematic flow chart of the method for determining the Doppler reactivity of the fuel of a reactor according to the embodiments of the present application, as Figure 1 shown, the determination method comprises the following steps S1 to S5.

[0018] S1, determining a Doppler constant according to the change of the Doppler reactivity due to the change of the temperature of the fuel.

[0019] S2, obtaining a steady-state fuel component, a steady-state fuel mass and a steady-state fuel temperature of the reactor.

[0020] S3, determining an initial Doppler reactivity of the reactor according to the Doppler constant determined in the S1 step and the steady-state fuel component, the steady-state fuel mass and the steady-state fuel temperature obtained in the S2 step.

[0021] S4, updating the Doppler reactivity of the reactor at any transient time according to a transient fuel component, a transient fuel mass and a transient fuel temperature of the reactor.

[0022] S5, determining a transient Doppler reactivity within the transient time according to the initial Doppler reactivity determined in the S3 step and the updated Doppler reactivity determined in the S4 step.

[0023] The method provided by the embodiments of the present application determines the transient Doppler reactivity of the reactor within the transient time according to the initial Doppler reactivity of the reactor and the updated Doppler reactivity at any transient time, which can realize the calculation of the change of the Doppler reactivity with time in the transient process, has high precision, is beneficial to improve the calculation ability of the reactivity feedback in the initial stage of fuel melting, and thus meets the analysis requirements for the severe accident of the sodium-cooled fast neutron nuclear reactor.

[0024] In some embodiments, in the S1 step, based on the perturbation theory, the three-dimensional fuel Doppler constant distribution is determined, and then the Doppler reactivity change caused by the temperature change of the fuel is determined according to 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] Wherein, 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 temperature change of the fuel in the grid; T represents the fuel temperature; m fuel (i,j,k) represents the fuel mass in the grid.

[0028] The method provided by the embodiments of the present application has high accuracy and reliability in determining the Doppler constant through the above expression (1).

[0029] In some embodiments, before the S3 step, the method further comprises: performing grid division on the reactor to obtain a plurality of grids; and in the S3 step, the initial Doppler reactivity of the reactor comprises the corresponding grid initial Doppler reactivity in each grid in the reactor.

[0030] The method provided by the embodiments of the present application has high accuracy in determining the grid initial Doppler reactivity by performing grid division on the reactor to obtain a plurality of grids, and then determining the corresponding grid initial Doppler reactivity in each grid.

[0031] In some embodiments, the S4 step comprises: S41, 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 at any transient moment; and S42, determining the updated Doppler reactivity of the updated reactor according to the updated Doppler reactivity of each grid.

[0032] The method provided by the embodiments of the present application further ensures the accuracy of the updated Doppler reactivity of the updated reactor by updating the Doppler reactivity of the grid at any transient moment, and then determining the updated Doppler reactivity of the updated reactor according to the updated Doppler reactivity of each grid.

[0033] In some embodiments, in the step S3, the initial Doppler reactivity at the steady state moment 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] wherein (i,j,k) represents a position of any grid in the reactor; Δρ Doppler,t0 (i,j,k) represents a change of the Doppler reactivity 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, the steady state fuel mass including 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, the steady state fuel temperature including the steady state solid fuel temperature and the steady state liquid fuel temperature.

[0036] The method provided by the embodiments of the present application has high efficiency by determining the initial Doppler reactivity at the steady state moment through the above expression (2).

[0037] In some embodiments, when the fuel is not melted, the steady state liquid fuel mass is zero, but 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 steady state temperatures T0 in all grids have the same value, so as to avoid the calculation result from being suddenly changed when the fuel moves.

[0039] In such embodiments, the steady state temperature T0 can be the average temperature of the fuel at the steady state moment.

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

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

[0042] wherein (i,j,k) represents a position of any grid in the reactor; Δρ Doppler,t (i,j,k) represents a change of the Doppler reactivity in the grid due to a change of the temperature 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, the transient fuel mass including the transient solid fuel mass and the transient liquid fuel mass; a fD (i,j,k) represents the Doppler constant in the grid; T0represents 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, the transient fuel temperature including the transient solid fuel temperature and the transient liquid fuel temperature.

[0043] The method provided by the embodiments of the present application updates the initial Doppler reactivity at the steady-state moment through the above expression (3), so as to ensure the accuracy of the updated Doppler reactivity.

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

[0045]

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

[0047] The method provided by the embodiment of the application determines the transient Doppler reactivity of the reactor through the above expression (4), and is beneficial to ensuring the reliability of the obtained change in the Doppler reactivity of the reactor at the transient moment.

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

[0049]

[0050] wherein P g represents the reactivity introduced by the gth group in a unit volume; represents the conjugate neutron flux density of the gth group; δ represents a change amount; D g represents the diffusion coefficient of the gth group; φ g represents the neutron flux density of the gth group; g represents the number of the neutron energy group; r represents removal of the group; g' represents the number of other groups except the 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 the 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 per fission; f represents the fission reaction; and V represents the volume of the calculation unit.

[0051] The method provided by the embodiment of the application determines the change in the Doppler reactivity due to the temperature change of the fuel through the above expression (5), and can determine the change in the Doppler reactivity with spatial distribution in the case of fuel production form change and movement behavior.

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

[0053] In some embodiments, the transient Doppler reactivity of the reactor can be determined by summing up the transient Doppler reactivity in each mesh.

[0054] In such embodiments, 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] wherein ρ(t) represents the total reactivity of the reactor; t represents a transient time; ρ fb,other (t) represents other reactivity except the 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 reactor neutron kinetics equations satisfy the following expressions (7) and (8):

[0058]

[0059] wherein N(t) represents the fission power of the core of the reactor; t represents a 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 decay time constant of the i-th group of delayed neutrons; C i (t) represents the i-th group of delayed neutron precursor concentration; β i represents the i-th group of delayed neutron fraction.

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

[0061] In some embodiments, according to the determination of the power change of the reactor, the thermal-hydraulic calculation is re-performed, and the transient fuel composition, the transient fuel mass and the transient fuel temperature of the reactor at the next transient time can be determined, and the 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 time.

[0062] In some embodiments, after the step S5, further comprising: 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 great influence on the Doppler reactivity, the Doppler reactivity in the sodium boiling condition can 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] wherein, Δρ Doppler (t) represents the corrected transient Doppler reactivity; a1 represents the Doppler constant of the non-empty reactor; a2 represents the Doppler constant of the full-empty reactor; α Void,t represents the sodium void fraction in the reactor at the transient moment; Δρ Doppler (t) represents the uncorrected transient Doppler reactivity.

[0067] The method provided by the embodiments of the present application corrects the determined transient Doppler reactivity by using the above expression (9), so as to further improve the accuracy of the obtained transient Doppler reactivity.

[0068] In such embodiments, the effect of the coolant void on the neutron leakage is corrected by linear adjustment of the input Doppler constants in the non-empty and void conditions.

[0069] For the embodiments of the present application, it should also be noted that the features of the embodiments of the present application and the embodiments can be combined with each other to obtain new embodiments without conflict.

[0070] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method of determining the Doppler reactivity of the fuel of a reactor, characterized in that, It comprises the following steps: S1, determining a Doppler constant according to a Doppler reactivity change 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 an initial Doppler reactivity of the reactor according to the Doppler constant determined in the S1 step and the steady-state fuel component, the steady-state fuel mass and the steady-state fuel temperature obtained in the S2 step; S4, updating the Doppler reactivity of the reactor according to a transient fuel component, a transient fuel mass and a transient fuel temperature of the reactor at any transient moment; S5, determining a transient Doppler reactivity at the transient moment according to the initial Doppler reactivity determined in the S3 step and the updated Doppler reactivity determined in the S4 step; In the S3 step, the initial Doppler reactivity at the steady-state moment satisfies the following expression: ； wherein, represents a location of any grid in the reactor; represents a Doppler reactivity change within the grid due to temperature changes of the fuel at a steady state time; represents a steady state solid fuel mass within the grid at the steady state time; represents a steady state liquid fuel mass within the grid at the steady state time, the steady state fuel mass comprising the steady state solid fuel mass and the steady state liquid fuel mass; represents a Doppler constant within the grid; T 0 represents a steady state temperature; represents a steady state solid fuel temperature within the grid at the steady state time; represents a steady state liquid fuel temperature within the grid at the steady state time, the steady state fuel temperature comprising the steady state solid fuel temperature and the steady state liquid fuel temperature; In the S4 step, the updated Doppler reactivity satisfies the following expression: ； wherein, represents a location of any grid in the reactor; represents a Doppler reactivity change within the grid due to a temperature change of the fuel at a transient time instant; represents a transient solid fuel mass within the grid at the transient time instant; represents a transient liquid fuel mass within the grid at the transient time instant, the transient fuel mass comprising the transient solid fuel mass and the transient liquid fuel mass; represents a Doppler constant within the grid; T 0 represents the steady state temperature; represents a transient solid fuel temperature within the grid at the transient time instant; represents a transient liquid fuel temperature within the grid at the transient time instant, the transient fuel temperature comprising the transient solid fuel temperature and the transient liquid fuel temperature; In the S5 step, the transient Doppler reactivity satisfies the following expression: ； wherein, represents the position of any grid in the reactor; represents the transient Doppler reactivity; t represents the transient time instant; represents the change in Doppler reactivity within the grid due to the temperature change of the fuel at the transient time instant; represents the change in Doppler reactivity within the grid due to the temperature change of the fuel at the steady state time instant; In the S1 step, the Doppler reactivity change caused by the temperature change of the fuel satisfies the following expression: ； wherein, denotes the g reactivity introduced by the group per unit volume; denotes the g conjugate neutron flux density of the group; δ denotes the change amount; D g denotes the g diffusion coefficient of the group; denotes the g neutron flux density of the group; g denotes the number of neutron energy groups; r denotes the removal from the group; denotes the number of other groups except the group; s denotes the scattering; k denotes the effective multiplication factor; denotes the g neutron production spectrum of the group; denotes the g conjugate neutron flux density of the group; denotes the Doppler reactivity change due to the temperature change of the fuel; G denotes the total number of neutron energy groups; v denotes the number of neutrons produced per fission; f denotes the fission reaction; V denotes the volume of the calculation unit; The Doppler constant satisfies the following expression: ； wherein, represents a Doppler constant within the mesh; represents a fuel temperature within the mesh; ρ represents a Doppler reactivity change due to a fuel temperature change within the mesh; T represents a fuel temperature; represents a fuel mass within the mesh.

2. The method of claim 1, wherein, Before the S3 step, further comprising: performing mesh division on the reactor to obtain a plurality of meshes; In the S3 step, the initial Doppler reactivity of the reactor comprises corresponding mesh initial Doppler reactivities in each mesh in the reactor.

3. The method of claim 2, wherein, The S4 step comprises: S41, updating the Doppler reactivity of each mesh according to the transient fuel component, the transient fuel mass and the transient fuel temperature in each mesh of the reactor at any transient moment; S42, determining the updated Doppler reactivity of the reactor according to the updated Doppler reactivity of each mesh.

4. The method according to any one of claims 1 to 3, characterized in that, After the S5 step, further comprising: correcting the transient Doppler reactivity.

5. The method of claim 4, wherein, The corrected transient Doppler reactivity satisfies the following expression: ； wherein, represents the modified transient Doppler reactivity; represents the Doppler constant of the reactor at full power; represents the Doppler constant of the reactor at full power; represents the sodium void fraction in the reactor at the transient time; represents the unmodified transient Doppler reactivity.

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