CN111048221B - Method for accurately obtaining reactivity feedback change in fast neutron reactor transient process - Google Patents

Method for accurately obtaining reactivity feedback change in fast neutron reactor transient process Download PDF

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CN111048221B
CN111048221B CN201911362830.8A CN201911362830A CN111048221B CN 111048221 B CN111048221 B CN 111048221B CN 201911362830 A CN201911362830 A CN 201911362830A CN 111048221 B CN111048221 B CN 111048221B
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reactivity
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CN111048221A (en
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郑友琦
贾晓茜
王永平
吴宏春
翟梓安
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Xian Jiaotong University
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    • G—PHYSICS
    • G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
    • G21C—NUCLEAR REACTORS
    • G21C17/00—Monitoring; Testing ; Maintaining
    • G21C17/10—Structural combination of fuel element, control rod, reactor core, or moderator structure with sensitive instruments, e.g. for measuring radioactivity, strain
    • G21C17/104—Measuring reactivity
    • G—PHYSICS
    • G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
    • G21C—NUCLEAR REACTORS
    • G21C17/00—Monitoring; Testing ; Maintaining
    • G21C17/10—Structural combination of fuel element, control rod, reactor core, or moderator structure with sensitive instruments, e.g. for measuring radioactivity, strain
    • G21C17/108—Measuring reactor flux
    • G—PHYSICS
    • G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
    • G21C—NUCLEAR REACTORS
    • G21C17/00—Monitoring; Testing ; Maintaining
    • G21C17/10—Structural combination of fuel element, control rod, reactor core, or moderator structure with sensitive instruments, e.g. for measuring radioactivity, strain
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Abstract

A method for accurately obtaining reactivity feedback change in a fast neutron reactor transient process considers the spatial distribution of reactivity feedback, obtains accurate fuel temperature reactivity feedback change, coolant density reactivity feedback change, axial expansion reactivity feedback change, radial expansion reactivity feedback change, assembly bending reactivity feedback change and control rod driving mechanism expansion reactivity feedback change in the transient process, and finally obtains three-dimensional reactivity feedback quantity in the fast neutron reactor transient process; the method has strong universality and wide application range, can accurately simulate the transient process of the reactor, reduces the calculation time, and provides accurate and reliable reactivity feedback parameters for the design task of the reactor core.

Description

Method for accurately obtaining reactivity feedback change in fast neutron reactor transient process
Technical Field
The invention belongs to the technical field of nuclear reactor engineering, and particularly relates to a method for accurately obtaining reactivity feedback change in a fast neutron reactor transient process.
Background
In order to rapidly analyze the transient accident process of the fast neutron reactor, a point reactor dynamics method based on a point reactor equation becomes a main method for fast reactor transient analysis according to the characteristics of the fast neutron reactor.
Figure GDA0003087263480000011
In the formula:
n (t) -neutron density in reactor at time t
Reactivity of the reactor at time p (t) -t
Beta-effective delayed neutron fraction
Λ -middle filial generation time
λiDecay constant of the i-th group of delayed neutrons
Ci(t) -concentration of precursor nucleus of slow-release neutron in ith group at t moment
βi-fraction of delayed neutrons in group i
According to the point reactor dynamics method, the effective delayed neutron share, the time of the intermediate offspring, the decay constant of the delayed neutron and the delayed neutron share are all obtained by the steady-state calculation of the reactor and do not change in the whole transient process; the changes are the reactor core reactivity, the in-reactor neutron density and the delayed neutron precursor nuclear concentration. Due to the fact that the temperature and the density of each material are changed in the transient process, the neutron characteristics, the change of the geometric dimension and the change of the relative position of the materials introduce reactivity feedback to the reactor, and the reactivity of the reactor core is changed; the change in core reactivity in turn results in a change in-core neutron density and delayed neutron precursor concentration.
To solve for the introduced reactivity feedback, the method of calculating the reactivity feedback coefficient using the "direct method" becomes the main method matching the "point pile dynamics". The first step of the direct method is to perform a first steady state calculation of the initial state of the reactor core and a second steady state calculation after the state of the reactor core is changed aiming at a kind of reactivity feedback, and the reactivity feedback coefficient of the reactor is obtained by dividing the reactivity variation of the reactor core obtained by the two calculations by the equivalent temperature of the state change of the reactor core; and the second step is that in the transient process, the change quantity of the equivalent temperature of the reactor core state at each moment is multiplied by the reactivity feedback coefficient to obtain the change quantity introduced by the reactivity feedback of the moment to the reactor core. And feeding back all kinds of reactivities to be considered to the reactor core reactivity, adding the introduced variable quantity and the reactivity of the initial state of the reactor core, obtaining the reactor core reactivity at the moment, and solving the equation updating parameters.
The direct method considers the whole reactor as a whole, so that the single-channel model becomes a method matched with the single-channel model for solving the thermal parameters of the reactor core. The average temperature of each material of the reactor core is obtained by solving a related thermal equation, and the change quantity of the equivalent temperature of the reactor core state at each moment is given. The direct method is combined with a single-channel model, and reactivity feedback caused by four reasons of fuel temperature change, coolant density change, axial geometric expansion of a reactor core and radial geometric expansion of the reactor core can be obtained. Due to the characteristics of the 'point reactor dynamics' method and the fact that the direct method and the single-channel model greatly simplify reactor modeling, the transient analysis method formed by combining the three methods is high in calculation efficiency and short in calculation time.
The reason for the introduction of reactivity during reactive transients is complex and diverse. In a fast neutron reactor, the reactor core is greatly deformed due to the change of the temperature of materials, the reactor assembly is bent, and at the moment, a single reactivity feedback coefficient and equivalent temperature are used, so that the reactivity feedback introduced by the bending of the assembly cannot be simulated, and therefore, the deformation and the reactivity feedback at different positions and different sections of the reactor in the process can be accurately analyzed by combining a mechanical model; meanwhile, a control rod driving mechanism positioned outside the reactor is also expanded by heat, so that the rod position of the control rod in the reactor core becomes smaller after the expansion, the control rod is inserted deeper, and the reactivity is introduced. Therefore, the model combining the direct method and the single-channel model cannot accurately consider the spatial distribution of the reactivity feedback, and can only obtain the reactivity feedback caused by four reasons, namely fuel temperature change, coolant density change, axial geometric expansion of a reactor core and radial geometric expansion of the reactor core.
In order to simulate the change of the reactivity feedback in the transient process more truly, the invention needs to invent a method which can take the spatial distribution of the reactivity feedback into consideration on the basis of the 'point reactor dynamics' method and can calculate the reactivity introduction caused by the expansion of the control rod driving mechanism so as to obtain the change of the reactivity feedback in the transient process more accurately.
Disclosure of Invention
In order to simulate the change of reactivity feedback in the transient process more truly, the invention aims to provide a method for accurately obtaining the change of the reactivity feedback in the transient process of a fast neutron reactor. The method can calculate the fuel temperature reactivity feedback, the coolant density reactivity feedback, the axial expansion reactivity feedback and the radial expansion reactivity feedback on each segment, and can calculate the bending deformation quantity of each segment of the reactor assembly and the deformation quantity of the control rod driving mechanism, thereby obtaining the bending reactivity feedback and the control rod driving mechanism expansion reactivity feedback, and more accurately obtaining the change of the reactivity feedback in the transient process of the reactor.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a method for accurately obtaining reactivity feedback change in a fast neutron reactor transient process comprises the following steps:
step 1: reading the geometric information of any fast reactor assembly, the material composition information and the quality information of the segment, and the nuclear density of various nuclides in the segment;
step 2: calculating reactivity changes caused by 1% of fuel temperature change and 1% of coolant density change according to a first-order perturbation theory aiming at the material component information read in the step 1 and the nuclear density of various nuclides:
Figure GDA0003087263480000041
in the formula:
phi-neutron flux density
φ*Neutron conjugated flux density
Delta rho-amount of change in reactivity before and after disturbance
keff-effective proliferation factor
F, S, A-fission, scattering and total extinction operator
dF, dS, dA-fission, scatter, and total vanishing operator of disturbance variables
Dividing the reactivity change before and after the disturbance of the fuel temperature of each segment by the equivalent temperature change to obtain the fuel temperature reactivity feedback coefficient alpha of each segmentD(i, j); dividing the front and back reactivity change of the disturbed coolant density of each segment by the density change to obtain the coolant density reactivity feedback coefficient alpha of each segmentC(i,j)：
Figure GDA0003087263480000051
In the formula:
αD(i, j) -ith channel jth nodal block fuel temperature reactivity feedback coefficient
αC(i, j) -ith channel jth nodal coolant density reactive feedback coefficient
ΔρD(i, j) — reactivity change Δ ρ before and after disturbance of fuel temperature by jth node of ith channelC(i, j) — the ith channel jth nub perturbs the coolant density before and after the reactivity change
Δ T (i, j) — jth nodal block fuel temperature change of ith passage
Δ v (i, j) — jth nodal coolant density variation for ith channel
For the reactivity introduced by axial expansion, materials are distinguished and a reactivity contribution R is introduced; under the condition of not changing the core segment, the nuclear density of a single material in the core segment is disturbed by 1% by mass, and the mass in each segment is calculatedReactivity contribution R of material per unit mass xx(i，j)：
Figure GDA0003087263480000052
In the formula:
Δρx(i, j) -change in reactivity of x material in the geometric region initially corresponding to the jth segment of the ith channel
Δmx(i, j) -change in mass of x material in the geometric region corresponding to the jth segment of the ith channel at the beginning
Rx(i, j) -reactive contribution of material per unit mass x
For the reactivity introduced by radial expansion, the increase of the temperature of a coolant inlet causes the expansion of a core lower positioning grid, at the moment, the radial geometric dimension of the core becomes larger, the density of each material nucleus in a segment is changed, so the core reactivity is calculated under the condition that the radial dimension of the core is increased by 1 percent, the obtained reactivity is divided by the equivalent temperature change of the radial expansion of the core, and the feedback coefficient alpha of the whole-reactor radial expansion reactivity is obtainedRADIAL；
Because the temperature difference of the inner wall and the outer wall of the assembly along the radial direction of the reactor core, the assembly can be subjected to the action of thermal stress to cause the bending deformation of the assembly, the radial geometric dimension of the reactor core is increased at the moment, and the density of each material nucleus in the segment is changed, so the reactivity of the reactor core is calculated under the condition that the radial dimension of the reactor core is increased by 1 percent, the obtained reactivity is divided by the radial expansion amount of the reactor core, and the bending reactivity feedback coefficient alpha is obtainedBOW；
For control rod drive mechanism expansion reactivity feedback, the differential value curve of the control rod needs to be calculated. Calculating the reactivity of the reactor core when the obtained control rod set is fully inserted and fully extracted, calculating coefficients a and b of the obtained control rod set differential value curve according to a formula (4), and obtaining a formula (5) of the group control rod differential value w curve:
Figure GDA0003087263480000061
w(x)＝ax+bx2formula (5)
In the formula:
h-distance of movement of control rod group in full insertion and full lifting state
Delta ρ -change in core reactivity in fully inserted and fully extracted states of a set of control rods
a-coefficient of differential value curve of control rod group
b-coefficient of differential value curve of control rod group
x-position of control rod set
w-differential value of control rod set at x rod position
And step 3: and calculating the state of the reactor core before the transient state starts to obtain initial parameters.
And 4, step 4: starting transient calculation, and respectively calculating each reactivity feedback quantity according to the reactivity feedback coefficient, the reactivity contribution and the control rod differential value w curve calculated in the step 2 and the transient initial parameter obtained in the step 3 at each time step in the transient process;
according to the calculation result of the parallel multi-channel model, the fuel temperature reactivity feedback coefficient alpha of each segment is calculatedD(i, j) multiplying by the change in the nodal fuel temperature from the initial parameter to obtain a fuel temperature reactivity feedback; the coolant density reactivity feedback coefficient alpha of each segmentC(i, j) multiplying by the change in nub coolant density compared to the initial parameter to obtain coolant density reactivity feedback;
for axial expansion reactivity feedback, the reactivity feedback for each segment can be obtained by equation (6):
Figure GDA0003087263480000071
in the formula:
m (i, j) — the x material mass at the beginning of the jth segment of the ith channel
Figure GDA0003087263480000072
Reactivity contributed by x material remaining in original segment after axial expansion
Figure GDA0003087263480000073
Reactivity contributed by x material entering upper segment after axial expansion
m(i,j)Rx(i, j) -reactivity of x Material within Primary segment
For the reactivity introduced by two radial expansions, the first can obtain the linear expansion coefficients of the two materials from the temperatures of the fuel and the cladding, and calculate the volume change of the fuel and the cladding in the segment, thereby calculating the reduction of the coolant density in the segment; the coolant density reactivity feedback coefficient alpha of each segmentC(i, j) multiplying by the change in nub coolant density to obtain a reactive feedback quantity; the second radial expansion requires calculation of the expansion of the spacer grids at the lower part of the core caused by the increase of the coolant inlet temperature, and the expansion of the spacer grids at the lower part is reduced to the middle plane of the core under the condition that the deformation of the components is not generated, and the reaction feedback coefficient alpha of the expansion of the middle plane of the core and the radial expansion of the whole reactor is calculatedRADIALMultiplying to obtain a reactive feedback quantity;
for the reactivity feedback introduced by the bending of the assembly, the bending reactivity feedback coefficient alpha is converted according to the nodal power distribution of the reactor coreBOWDistributed to each segment to obtain the bending reactivity feedback coefficient alpha of each segmentBOW(i, j); the deformation of the bending of the assembly is obtained by establishing an assembly mechanical model, the assembly is integrally regarded as a beam, and an elastic curve differential equation of the beam is solved:
Figure GDA0003087263480000081
in the formula:
e-modulus of elasticity of the Material of the component cassette
I-component moment of inertia
x-distance along the beam
y-offset of the component at x relative to an axis perpendicular to the bottom surface of the component
MxThermal stress to which the assembly is subjected at x
m-total mass of component box material in the assembly
l-total length of the assembly
Figure GDA0003087263480000091
-average value of coefficient of linear expansion of inner and outer wall assembly box material of assembly along radius direction of reactor core
TDUCT,OUTTemperature of the assembly box along the radial outer wall of the core
TDUCT,INTemperature of assembly box with assembly along radial inner wall of core
a-facing margin of outer wall of assembly box
Because the components receive different constraint positions and different constraint types, the solutions of the elastic curve differential equations of the beams are various, but the solution in each case is a definite solution; the offset y (i, j) of each segment relative to an axis perpendicular to the bottom surface of the component, obtained from the mechanical model, is compared with the bending reactivity feedback coefficient alpha of each segmentBOW(i, j) multiplying to obtain the bending reactivity feedback quantity of each segment;
for the reactivity feedback due to the expansion of the control rod drive mechanism, the amount of control rod plunging due to expansion needs to be calculated. Establishing a convection heat exchange equation of the control rod driving mechanism and the surrounding coolant:
Figure GDA0003087263480000092
in the formula:
Mcrthe mass of the control rod drive mechanism
CcrSpecific heat capacity of control rod drive mechanism material
TcrTemperature of the control rod drive mechanism
t-time variable
hcr-heat transfer coefficient of control rod drive mechanism material
Acr-heat exchange area of control rod drive mechanism with surrounding coolant
TuiTemperature of coolant surrounding the control rod drive mechanism
wc-the control rod drive mechanism corresponding to the assembly channel flow rate
Tmm-coolant outlet mixing temperature
ρuDensity of coolant around control rod drive mechanism
VuiVolume of coolant surrounding the control rod drive mechanism
The temperature T of the control rod drive mechanism at this time can be obtainedcrThe expansion amount of the control rod driving mechanism can be obtained according to the variation of the temperature of the control rod driving mechanism; and combining the obtained axial expansion of the core, the control rod downward insertion amount can be obtained. And (4) obtaining the control rod differential value at the current rod position according to the control rod differential value curve calculated in the step (2). Multiplying the differential value of the control rod at the current rod position by the control rod downward insertion amount to obtain the reactivity feedback amount caused by the expansion of the control rod driving mechanism;
and 5: and (4) adding all the reactivity feedback quantities obtained in the step (4) to obtain a three-dimensional reactivity feedback quantity in the transient process of the fast neutron reactor.
Compared with the prior art, the invention has the following outstanding advantages:
1. in the method, the thermotechnical parameters are calculated by a parallel multi-channel model, so that the use of average parameters of the whole reactor is avoided; a reactivity feedback model considering the spatial distribution of the reactivity feedback is introduced, so that the high precision of the calculation of the reactivity feedback is ensured;
2. in the method, the concept of reactivity contribution is provided, the axial expansion reactivity feedback can be calculated under the condition of not changing the block geometry, and the high efficiency of calculation is ensured;
3. in the method, a component mechanical model and a control rod driving mechanism and a convection heat exchange model of surrounding coolant are established, so that the requirement of calculating the reactivity feedback caused by the bending reactivity feedback of the component and the expansion of the control rod driving mechanism is met, and more complete reactivity feedback is obtained.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic view of the deformation of the axial expansion joint of the assembly.
Fig. 3 is a schematic view of the bending deformation of the assembly.
FIG. 4 is a control rod drive mechanism expansion schematic.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
the method considers the reactivity feedback spatial distribution, utilizes a first-order perturbation theory to carefully consider the reactivity feedback change of each segment of the fast reactor assembly, and calculates the accurate fuel temperature reactivity feedback and coolant density reactivity feedback of each segment; the concept of reactivity contribution is provided, and the axial expansion reactivity feedback of each segment of the fast reactor assembly is calculated finely; introducing a mechanical model, calculating the bending offset of the fast reactor assembly, and accurately calculating the bending reactivity feedback of each segment of the assembly; and introducing a convective heat transfer model, taking the influence of the expansion of the control rod drive mechanism on the reactivity into consideration, and calculating reactivity feedback caused by the expansion of the control rod drive mechanism. As shown in fig. 1, the present invention comprises the steps of:
step 1: reading the geometric information of any fast reactor assembly, the material composition information and the quality information of the segment, and the nuclear density of various nuclides in the segment;
step 2: calculating reactivity changes caused by 1% of fuel temperature change and 1% of coolant density change according to a first-order perturbation theory aiming at the material component information read in the step 1 and the nuclear density of various nuclides:
Figure GDA0003087263480000121
in the formula:
phi-neutron flux density
φ*Neutron conjugated flux density
Delta rho-amount of change in reactivity before and after disturbance
keff-effective proliferation factor
F, S, A-fission, scattering and total extinction operator
dF, dS, dA-fission, scatter, and total vanishing operator of disturbance variables
Dividing the reactivity change before and after the disturbance of the fuel temperature of each segment by the equivalent temperature change to obtain the fuel temperature reactivity feedback coefficient alpha of each segmentD(i, j); dividing the front and back reactivity change of the disturbed coolant density of each segment by the density change to obtain the coolant density reactivity feedback coefficient alpha of each segmentC(i,j)：
Figure GDA0003087263480000122
In the formula:
αD(i, j) -ith channel jth nodal block fuel temperature reactivity feedback coefficient
αC(i, j) -ith channel jth nodal coolant density reactive feedback coefficient
ΔρD(i, j) — reactivity change Δ ρ before and after disturbance of fuel temperature by jth node of ith channelC(i, j) — the ith channel jth nub perturbs the coolant density before and after the reactivity change
Δ T (i, j) — jth nodal block fuel temperature change of ith passage
Δ v (i, j) — jth nodal coolant density variation for ith channel
For the reactivity introduced by axial expansion, the materials are distinguished and a reactivity contribution R is introduced. Under the condition of not changing the core segment, the nuclear density of a single material is disturbed by 1% of mass, and the reactivity contribution R of the material per unit mass x in each segment is calculatedx(i，j)：
Figure GDA0003087263480000131
In the formula:
Δρx(i, j) -change in reactivity of x material in the geometric region initially corresponding to the jth segment of the ith channel
Δmx(i, j) -change in mass of x material in the geometric region corresponding to the jth segment of the ith channel at the beginning
Rx(i, j) -reactive contribution of material per unit mass x
For the reactivity introduced by radial expansion, the increase of the temperature of a coolant inlet causes the expansion of a core lower positioning grid, at the moment, the radial geometric dimension of the core becomes larger, the density of each material nucleus in a segment is changed, so the core reactivity is calculated under the condition that the radial dimension of the core is increased by 1 percent, the obtained reactivity is divided by the equivalent temperature change of the radial expansion of the core, and the feedback coefficient alpha of the whole-reactor radial expansion reactivity is obtainedRADIAL。
Because the temperature difference of the inner wall and the outer wall of the assembly along the radial direction of the reactor core, the assembly can be subjected to the action of thermal stress to cause the bending deformation of the assembly, the radial geometric dimension of the reactor core is increased at the moment, and the density of each material nucleus in the segment is changed, so the reactivity of the reactor core is calculated under the condition that the radial dimension of the reactor core is increased by 1 percent, the obtained reactivity is divided by the radial expansion amount of the reactor core, and the bending reactivity feedback coefficient alpha is obtainedBOW。
For control rod drive mechanism expansion reactivity feedback, the differential value curve of the control rod needs to be calculated. Calculating the reactivity of the reactor core when the obtained control rod set is fully inserted and fully extracted, calculating coefficients a and b of the obtained control rod set differential value curve according to a formula (4), and obtaining a formula (5) of the group control rod differential value w curve:
Figure GDA0003087263480000141
w(x)＝ax+bx2formula (5)
In the formula:
h-distance of movement of control rod group in full insertion and full lifting state
Delta ρ -change in core reactivity in fully inserted and fully extracted states of a set of control rods
a-coefficient of differential value curve of control rod group
b-coefficient of differential value curve of control rod group
x-position of control rod set
w-differential value of control rod set at x rod position
And step 3: and calculating the state of the reactor core before the transient state starts to obtain initial parameters.
And 4, step 4: transient state calculations begin. And (3) respectively calculating each reactivity feedback quantity at each time step in the transient process according to the reactivity feedback coefficient, the reactivity contribution and the control rod differential value curve calculated in the step (2) and the transient initial parameter obtained in the step (3).
According to the calculation result of the parallel multi-channel model, the fuel temperature reactivity feedback coefficient alpha of each segment is calculatedD(i, j) multiplying by the change in the nodal fuel temperature from the initial parameter to obtain a fuel temperature reactivity feedback; the coolant density reactivity feedback coefficient alpha of each segmentC(i, j) times the change in nodal coolant density compared to the initial parameter to obtain coolant density reactivity feedback.
For axial expansion reactivity feedback, as shown in FIG. 2, the distance from the initial upper and lower surfaces of each segment to the bottom of the core is represented by z0The distance from the expanded upper and lower surfaces to the bottom of the core is represented by znRepresents, i.e.: the distance from the initial lower surface of the jth node of the ith channel to the bottom of the reactor core is z0(i, j) the distance of the upper surface from the bottom of the core is z0(i, j + 1); the distance from the lower surface of the expanded segment to the bottom of the reactor core is zn(i, j) the distance of the upper surface from the bottom of the core is zn(i, j + 1). The reactivity feedback for the jth segment of the ith channel can be obtained by equation (6):
Figure GDA0003087263480000151
in the formula:
m (i, j) — the x material mass at the beginning of the jth segment of the ith channel
Figure GDA0003087263480000152
Reactivity contributed by x material remaining in original segment after axial expansion
Figure GDA0003087263480000153
Reactivity contributed by x material entering upper segment after axial expansion
m(i,j)Rx(i, j) -reactivity of x Material within Primary segment
For the reactivity introduced by two radial expansions, the first can obtain the linear expansion coefficients of the two materials from the temperatures of the fuel and the cladding, and calculate the volume change of the fuel and the cladding in the segment, thereby calculating the reduction of the coolant density in the segment; the coolant density reactivity feedback coefficient alpha of each segmentC(i, j) times the amount of change in nodal coolant density to obtain the amount of reactive feedback. The second radial expansion requires calculation of the expansion of the spacer grids at the lower part of the core caused by the increase of the coolant inlet temperature, and the expansion of the spacer grids at the lower part is reduced to the middle plane of the core under the condition that the deformation of the components is not generated, and the reaction feedback coefficient alpha of the expansion of the middle plane of the core and the radial expansion of the whole reactor is calculatedRADIALAnd multiplying to obtain the reactive feedback quantity.
For reactivity feedback introduced by component bending, firstly, a bending reactivity feedback coefficient alpha is determined according to the nodal power distribution of a reactor coreBOWDistributed to each segment to obtain the bending reactivity feedback coefficient alpha of each segmentBOW(i, j). The deformation amount of the bending of the component is obtained by establishing a mechanical model of the component, as shown in fig. 3: will the subassemblyThe whole body is regarded as a beam, the temperature of the inner wall and the outer wall of the assembly along the radius direction of the reactor core is different, so that the expansion amount of the inner wall and the outer wall is different, and the bending moment generated causes the bending deformation of the assembly. Solving the spring curve differential equation for the beam yields the offset of the assembly at different heights from an axis perpendicular to the bottom surface of the assembly:
Figure GDA0003087263480000161
in the formula:
e-modulus of elasticity of the Material of the component cassette
I-component moment of inertia
x-distance along the beam
y-offset of the component at x relative to an axis perpendicular to the bottom surface of the component
MxThermal stress to which the assembly is subjected at x
m-total mass of component box material in the assembly
l-total length of the assembly
Figure GDA0003087263480000171
-average value of coefficient of linear expansion of inner and outer wall assembly box material of assembly along radius direction of reactor core
TDUCT,OUTTemperature of the assembly box along the radial outer wall of the core
TDUCT,INTemperature of assembly box with assembly along radial inner wall of core
a-facing margin of outer wall of assembly box
The upper core load plate and the upper core load plate shown in fig. 3 represent structures for fixing and supporting the assemblies at the upper portions of the core and the active region, which generate constraints on the bending deformation of the assemblies. There are also a number of solutions to the differential equation of the spring curve for the beam, due to the different locations and types of constraints received by the assembly, but the solution in each case is a fixed solution. Of each segment obtained from the mechanical model with respect to an axis perpendicular to the bottom surface of the componentOffset y (i, j), and bending reactivity feedback coefficient alpha of each segmentBOW(i, j) are multiplied to obtain the bending reactivity feedback quantity of each segment.
For the reactivity feedback caused by the expansion of the control rod drive mechanism, as shown in fig. 4, the control rod drive mechanism is subjected to the scouring of the surrounding high-temperature coolant to cause the temperature to rise and expand, so that the control rod is inserted downwards in the core; the increase in core temperature causes axial core expansion, which results in a change in the relative position of the control rods to the core, which is equivalent to control rod plunge. The two are combined to obtain the control rod inserting amount. Establishing a convection heat exchange equation of the control rod driving mechanism and surrounding coolant to obtain the current temperature of the control rod driving mechanism:
Figure GDA0003087263480000172
in the formula:
Mcrthe mass of the control rod drive mechanism
CcrSpecific heat capacity of control rod drive mechanism material
TcrTemperature of the control rod drive mechanism
t-time variable
hcr-heat transfer coefficient of control rod drive mechanism material
Acr-heat exchange area of control rod drive mechanism with surrounding coolant
TuiTemperature of coolant surrounding the control rod drive mechanism
wc-the control rod drive mechanism corresponding to the assembly channel flow rate
Tmm-coolant outlet mixing temperature
ρuDensity of coolant around control rod drive mechanism
VuiVolume of coolant surrounding the control rod drive mechanism
The temperature T of the control rod drive mechanism at this time can be obtainedcrThe amount of expansion of the control rod drive mechanism can be obtained from the amount of change in temperature of the control rod drive mechanism. And (4) obtaining the control rod differential value at the current rod position according to the control rod differential value curve calculated in the step (2). And multiplying the differential value of the control rod at the current rod position by the control rod inserting amount to obtain the reactivity feedback amount caused by the expansion of the control rod driving mechanism.
And 5: and (4) adding all the reactivity feedback quantities obtained in the step (4) to obtain a three-dimensional reactivity feedback quantity in the transient process of the fast neutron reactor.
In the invention, the geometric and material information of any fast reactor assembly is read in by step 1, and the mechanical parameters of the assembly and the related physical properties of each material are obtained by processing the information read in by step 1 through step 3. The mechanical parameter calculation relational expression of the component and the physical property calculation relational expression of each material can be added according to the geometry of the component and the material. The invention is not limited to the choice of component types and materials.
The various reaction feedback coefficients calculated in the step 2 are applicable to transient analysis of any type of fast neutron reactor, and the method is not limited by the type of the fast neutron reactor.
The downward insertion distance of the control rods caused by the expansion of the control rod drive mechanisms in the step 4 is related to the positioning mode of the control rod drive mechanisms, and the invention refers to the assumption that the control rod drive mechanisms are fixed at the top of the reactor vessel; if the control rod drive mechanism is suspended above the core, the distance of insertion of the control rods is only equal to the axial expansion of the core and does not need to be summed with the expansion of the control rod drive mechanism, but the control rod differential value curve and method of use remain applicable. The calculation method of the differential value curve of the control rod and the resultant reactivity feedback is not limited by the control rod fixing mode.
By utilizing the accurate reactivity feedback change, the fine analysis of the transient process of the fast reactor core can be carried out. The method can obtain high-precision reactivity feedback change and can be applied to the design and calculation of the fast reactor core.

Claims (1)

1. A method for accurately obtaining reactivity feedback change in a fast neutron reactor transient process is characterized by comprising the following steps: the method comprises the following steps:
step 1: reading the geometric information of any fast reactor assembly, the material composition information and the quality information of the segment, and the nuclear density of various nuclides in the segment;
step 2: calculating reactivity changes caused by 1% of fuel temperature change and 1% of coolant density change according to a first-order perturbation theory aiming at the material component information read in the step 1 and the nuclear density of various nuclides:
Figure FDA0003087263470000011
in the formula:
phi-neutron flux density
φ*Neutron conjugated flux density
Delta rho-amount of change in reactivity before and after disturbance
keff-effective proliferation factor
F, S, A-fission, scattering and total extinction operator
dF, dS, dA-fission, scatter, and total vanishing operator of disturbance variables
Dividing the reactivity change before and after the disturbance of the fuel temperature of each segment by the equivalent temperature change to obtain the fuel temperature reactivity feedback coefficient alpha of each segmentD(i, j); dividing the front and back reactivity change of the disturbed coolant density of each segment by the density change to obtain the coolant density reactivity feedback coefficient alpha of each segmentC(i,j)：
Figure FDA0003087263470000012
In the formula:
αD(i, j) -ith channel jth nodal block fuel temperature reactivity feedback coefficient
αC(i, j) -ith channel jth nodal block coldCoolant density reactive feedback coefficient
ΔρD(i, j) -reactivity change before and after fuel temperature disturbance of jth node of ith channel
ΔρC(i, j) — the ith channel jth nub perturbs the coolant density before and after the reactivity change
Δ T (i, j) — jth nodal block fuel temperature change of ith passage
Δ v (i, j) — jth nodal coolant density variation for ith channel
For the reactivity introduced by axial expansion, materials are distinguished and a reactivity contribution R is introduced; under the condition of not changing the core segment, the nuclear density of a single material is disturbed by 1% of mass, and the reactivity contribution R of the material per unit mass x in each segment is calculatedx(i，j)：
Figure FDA0003087263470000021
In the formula:
Δρx(i, j) -change in reactivity of x material in the geometric region initially corresponding to the jth segment of the ith channel
Δmx(i, j) -change in mass of x material in the geometric region corresponding to the jth segment of the ith channel at the beginning
Rx(i, j) -reactive contribution of material per unit mass x
For the reactivity introduced by radial expansion, the increase of the temperature of a coolant inlet causes the expansion of a core lower positioning grid, at the moment, the radial geometric dimension of the core becomes larger, the density of each material nucleus in a segment is changed, so the core reactivity is calculated under the condition that the radial dimension of the core is increased by 1 percent, the obtained reactivity is divided by the equivalent temperature change of the radial expansion of the core, and the feedback coefficient alpha of the whole-reactor radial expansion reactivity is obtainedRADIAL；
Because the temperature difference of the inner wall and the outer wall of the assembly along the radius direction of the reactor core, the assembly can be subjected to the action of thermal stress to cause the bending deformation of the assembly, at the moment, the radial geometric dimension of the reactor core becomes large, and the material nuclei in the segment blocks are denseSince the degree of change is generated, the reactivity of the core is calculated when the radial dimension of the core is increased by 1%, and the obtained reactivity change is divided by the radial expansion amount of the core to obtain the bending reactivity feedback coefficient alphaBOW；
For the control rod drive mechanism expansion reactivity feedback, the differential value curve of the control rod needs to be calculated; calculating the reactivity of the reactor core when the obtained control rod set is fully inserted and fully extracted, calculating coefficients a and b of the obtained control rod set differential value curve according to a formula (4), and obtaining a formula (5) of the group control rod differential value w curve:
Figure FDA0003087263470000031
w(x)＝ax+bx2formula (5)
In the formula:
h-distance of movement of control rod group in full insertion and full lifting state
Delta ρ -change in core reactivity in fully inserted and fully extracted states of a set of control rods
a-coefficient of differential value curve of control rod group
b-coefficient of differential value curve of control rod group
x-position of control rod set
w-differential value of control rod set at x rod position
And step 3: calculating the state of the reactor core before the transient state starts to obtain initial parameters;
and 4, step 4: starting transient calculation, and respectively calculating each reactivity feedback quantity according to the reactivity feedback coefficient, the reactivity contribution and the control rod differential value w curve calculated in the step 2 and the transient initial parameter obtained in the step 3 at each time step in the transient process;
according to the calculation result of the parallel multi-channel model, the fuel temperature reactivity feedback coefficient alpha of each segment is calculatedD(i, j) multiplying by the change in the nodal fuel temperature from the initial parameter to obtain a fuel temperature reactivity feedback; reactivating the coolant density of each segmentCoefficient of feed alphaC(i, j) multiplying by the change in nub coolant density compared to the initial parameter to obtain coolant density reactivity feedback;
for axial expansion reactivity feedback, the reactivity feedback for each segment is obtained from equation (6):
Figure FDA0003087263470000041
in the formula:
m (i, j) — the x material mass at the beginning of the jth segment of the ith channel
Figure FDA0003087263470000042
Reactivity contributed by x material remaining in original segment after axial expansion
Figure FDA0003087263470000043
Reactivity contributed by x material entering upper segment after axial expansion
m(i,j)Rx(i, j) -reactivity of x Material within Primary segment
For the reactivity introduced by two radial expansions, the first obtains the linear expansion coefficients of the two materials from the temperatures of the fuel and the cladding, calculates the volume change of the fuel and the cladding in the segment, and then calculates the reduction of the coolant density in the segment; the coolant density reactivity feedback coefficient alpha of each segmentC(i, j) multiplying by the change in nodal coolant density to obtain a reactive feedback quantity; the second radial expansion requires calculation of the expansion of the spacer grids at the lower part of the core caused by the increase of the coolant inlet temperature, and the expansion of the spacer grids at the lower part is reduced to the middle plane of the core under the condition that the deformation of the components is not generated, and the reaction feedback coefficient alpha of the expansion of the middle plane of the core and the radial expansion of the whole reactor is calculatedRADIALMultiplying to obtain a reactive feedback quantity;
for reactive feedback introduced by bending of the assembly, according toSegmental power distribution of reactor core, bending reactivity feedback coefficient alphaBOWDistributed to each segment to obtain the bending reactivity feedback coefficient alpha of each segmentBOW(i, j); the deformation of the bending of the assembly is obtained by establishing an assembly mechanical model, the assembly is integrally regarded as a beam, and an elastic curve differential equation of the beam is solved:
Figure FDA0003087263470000051
in the formula:
e-modulus of elasticity of the Material of the component cassette
I-component moment of inertia
x-distance along the beam
y-offset of the component at x relative to an axis perpendicular to the bottom surface of the component
MxThermal stress to which the assembly is subjected at x
m-total mass of component box material in the assembly
l-total length of the assembly
Figure FDA0003087263470000061
-average value of coefficient of linear expansion of inner and outer wall assembly box material of assembly along radius direction of reactor core
TDUCT,OUTTemperature of the assembly box along the radial outer wall of the core
TDUCT,INTemperature of assembly box with assembly along radial inner wall of core
a-facing margin of outer wall of assembly box
Because the components receive different constraint positions and different constraint types, the solutions of the elastic curve differential equations of the beams are various, but the solution in each case is a definite solution; the offset y (i, j) of each segment relative to an axis perpendicular to the bottom surface of the component, obtained from the mechanical model, is compared with the bending reactivity feedback coefficient alpha of each segmentBOW(i, j) multiplying to obtain a bending reactivity feedback quantity of each segment;
for the reactivity feedback caused by the expansion of the control rod drive mechanism, the amount of control rod insertion due to the expansion needs to be calculated; establishing a convection heat exchange equation of the control rod driving mechanism and the surrounding coolant:
Figure FDA0003087263470000062
in the formula:
Mcrthe mass of the control rod drive mechanism
CcrSpecific heat capacity of control rod drive mechanism material
TcrTemperature of the control rod drive mechanism
t-time variable
hcr-heat transfer coefficient of control rod drive mechanism material
Acr-heat exchange area of control rod drive mechanism with surrounding coolant
TuiTemperature of coolant surrounding the control rod drive mechanism
wc-the control rod drive mechanism corresponding to the assembly channel flow rate
Tmm-coolant outlet mixing temperature
ρuDensity of coolant around control rod drive mechanism
VuiVolume of coolant surrounding the control rod drive mechanism
The temperature T of the control rod drive mechanism at this time can be obtainedcrThe expansion amount of the control rod driving mechanism can be obtained according to the variation of the temperature of the control rod driving mechanism; the control rod downward insertion amount can be obtained by combining the obtained axial core expansion amount, the control rod differential value at the current rod position can be obtained by the control rod differential value curve calculated in the step 2, and the reactivity feedback amount caused by the expansion of the control rod driving mechanism is obtained by multiplying the control rod differential value at the current rod position by the control rod downward insertion amount;
and 5: and (4) adding all the reactivity feedback quantities obtained in the step (4) to obtain a three-dimensional reactivity feedback quantity in the transient process of the fast neutron reactor.
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