CN114692527B - Sodium-cooled fast reactor fragment bed migration criterion method - Google Patents
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Abstract
The invention discloses a sodium-cooled fast reactor fragment bed migration criterion method, which is characterized in that the stress analysis is carried out on fragment particles in a fragment bed by combining the density, the size, the shape and the position of the particles, meanwhile, the resultant force of liquid bridge force representing the action of liquid surface tension is introduced, a stress balance equation in a critical state in the migration process is obtained, the relative speed between the fragment particles with the action of liquid surface tension and fluid is obtained, the external fluid speed is considered, the relative speed between the fragment particles with the action of liquid surface tension and the fluid and the external fluid speed are compared, and whether the fragment bed is migrated or not is judged. The method can accurately predict the movement trend in the migration process of the fragment bed, effectively evaluate the migration characteristics of the lower cavity fragment bed in the disassembly accident of the sodium-cooled fast reactor core, and solve the problems of poor simulation effect and low credibility of the migration phenomenon of the previous fragment bed.
Description
Technical Field
The invention belongs to the technical field of nuclear reactor safety facility design, and particularly relates to a sodium-cooled fast reactor fragment bed migration criterion method.
Background
In the accident of the disassembly of the reactor core of the sodium-cooled fast reactor, molten reactor core fuel can diffuse to the lower cavity of the reactor core, and on one hand, the molten reactor core fuel can be quenched, solidified and dispersed into fragment particles under the action of coolant in the lower cavity; on the other hand, the particles of the debris bed are subjected to the action of gravity and accumulated on the surface of the reactor core melt collector of the lower reactor core chamber into a mound-like structure of the debris bed. Due to the effect of the decay heat of the fuel particles, the coolant in the fragment bed can be boiled, and the fragment particles migrate under the combined pushing action of sodium vapor and liquid sodium, so that the overall shape and thickness of the fragment bed are changed, and the migration and self-leveling processes can occur. If fuel chips accumulate excessively in the lower core cavity, the in-bed decay heat cannot be removed, resulting in molten particles melting through the core melt collector, damaging the integrity of the containment vessel, and even again inducing a re-critical event. Therefore, in order to ensure effective implementation of in-reactor-melt retention measures, research evaluations of the migration characteristics of the chip bed have to be carried out.
The migration of the fuel chip bed is a complex heat and mass transfer process involving solid, liquid and gas three-phase flow, and numerical simulation of the fuel chip bed is difficult. In the simulation process, the important point is to study the critical point at the initial moment of migration of the fragment particles and the stress analysis. The existing semi-empirical migration criterion method for simulating the migration behavior of the fragment bed has a plurality of defects, the simulation effect is poor, and the reliability is low.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a sodium-cooled fast reactor fragment bed migration criterion method which is used for effectively evaluating the migration characteristics of a lower cavity fragment bed in a reactor core disassembly accident of a sodium-cooled fast reactor by introducing the action of inter-particle liquid bridge in stress balance analysis to improve the prediction accuracy in a smaller particle size range.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a migration criterion model of a sodium-cooled fast reactor fragment bed is characterized in that stress analysis is carried out on fragment particles in the fragment bed by combining the density, the size, the shape and the position of the particles, meanwhile, liquid bridge force representing the action of liquid surface tension is introduced, according to the practical situation, the particles of the fragment bed possibly form liquid bridges with a plurality of particles in contact with the periphery of the particles at the same time, resultant force formed by the combined action of the liquid bridge force is obtained, a stress balance equation in a critical state in the migration process is obtained, the relative speed between the particles with the action of the liquid surface tension and fluid is obtained, and finally, the external fluid speed is considered, so that whether the migration phenomenon of the fragment bed occurs is judged.
Specifically, the vertical force balance equation borne by the chip particle units in the chip bed is as follows:
F D +F b ＝F g +F g combination
Wherein F is D For external fluid drag, F b For buoyancy of external fluid, F g For the self gravity of the particles F G combination Is the resultant force of liquid bridge force at the bottom of the particles.
Further, the debris particle unit is subjected to an external fluid drag force F D Buoyancy F of external fluid b And the self gravity F of the particles g The calculation is as follows:
wherein C is d For drag coefficient, d is particle diameter, ρ m Is the average density of gas-liquid two-phase flow, v' eq For the relative velocity between the particle and the fluid ρ p Particle density, g is gravitational acceleration.
At the same time, the resultant force F of liquid bridge force at the bottom of the particles G combination The calculation is as follows:
wherein F is G Is the liquid bridge force between particles, 2 pi R 2 σ T As a surface tension term,as capillary pressure term, sigma T Is the surface tension coefficient, ΔP is the capillary pressure difference, R 1 Is the contour radius of the liquid bridge, R 2 Is the radius of the neck of the liquid bridge.
Specifically, the liquid bridge contour radius R 1 And liquid bridge neck radius R 2 The calculation is as follows:
wherein a is the inter-particle distance, d is the particle diameter, θ c The contact angle between particles and liquid is shown, and delta is the liquid filling angle between particles.
In summary, the equilibrium equation is solved, taking into account the relative velocity v 'between the particles and the fluid under the action of the surface tension of the liquid' eq The calculation is as follows:
wherein ρ is p Is particle density ρ m Is the average density of gas-liquid two-phase flow, g is gravity acceleration, d is particle diameter, C d For drag coefficient, sigma T R is the surface tension coefficient 1 Is the contour radius of the liquid bridge, R 2 Is the radius of the neck of the liquid bridge.
Fluid flow velocity v g The calculation is as follows:
wherein Q is the gas injection flow rate, A is the fragment bed cross-sectional area, α g Epsilon is the porosity of the fragment bed, which is the flow cross-section average void fraction.
Further, the flow cross-section average cavitation fraction ε g The calculation is as follows:
wherein alpha is gExp A volume average void fraction of fluid within the debris bed;for the section void fraction correction coefficient, the average void fraction and the minimum (or maximum) effective void fraction of each group volume are obtained through experimental measurement, and the value of the section void fraction correction coefficient is obtained.
Further, the volume average void fraction alpha of the fluid in the chip bed gExp The calculation is as follows:
wherein DeltaV is the variation of the fluid volume, V p For the total volume of the chip bed portion, Δh is the variation value of the liquid level, h p Epsilon is the porosity of the bed of fragments, which is the average height of the bed of fragments.
Specifically, the judgment is as follows:
wherein v is g For external fluid flow velocity, v' eq Is the relative velocity between the particles and the fluid.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention provides a sodium-cooled fast reactor fragment bed migration criterion method, which is characterized in that the stress analysis is carried out on fragment particles in a fragment bed by combining the particle density, size, shape and position, meanwhile, the liquid bridge force representing the action of the liquid surface tension is introduced, according to the practical situation, the fragment particles of the fragment bed possibly form a liquid bridge with a plurality of fragment particles contacted with the periphery of the fragment particles at the same time, the liquid bridge force combining force at the bottom of the fragment particles formed by the combined action of the liquid bridge force is obtained, the vertical stress balance equation born by the fragment particles in the fragment bed in the critical state in the migration process is obtained, the relative speed between the fragment particles and fluid under the action of the liquid surface tension is obtained, the external fluid speed is considered finally, the relative speed between the particles and the fluid is compared, the size of the external fluid speed is compared, whether the migration phenomenon of the fragment bed occurs is judged, and the migration characteristic of the lower chamber fragment bed in the reactor core disassembly accident of the sodium-cooled fast reactor is effectively evaluated.
Further, the external fluid applied force and self gravity influence of the fragment particles in the fragment bed are calculated and analyzed, stress analysis is carried out, and factors such as the size, shape, position and density of the fragment particles are fully considered, so that a calculation result is real and reliable.
Further, the influence of liquid bridge force generated among the fragment particles in the fragment bed is analyzed, and the influence is introduced into an equilibrium state equation, so that the stress analysis is more reasonable.
Further, by solving an equilibrium state equation, the relative speed between the fragment particles and the fluid is obtained, so that the phase-to-phase equilibrium speed of the liquid bridge force is obtained.
Further, by solving the flow rate of the external fluid and comparing the flow rate with the relative speed between the fragment particles and the fluid, whether migration occurs or not is judged, and the migration characteristics of the lower cavity fragment bed in the sodium-cooled fast reactor core disintegration accident are effectively evaluated.
In conclusion, the method can accurately predict the movement trend of the migration of the fragment bed in the simulation of the migration phenomenon of the fragment bed of the sodium-cooled fast reactor by a simple method, improves the prediction accuracy in a smaller particle size range, effectively evaluates the migration characteristics of the fragment bed of the lower cavity in the disintegration accident of the reactor core of the sodium-cooled fast reactor, and solves the problems of poor simulation effect and low credibility of the migration phenomenon of the fragment bed in the prior art.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of the top layer particle stress balance state after the liquid bridge force is considered;
FIG. 3 is a schematic illustration of a liquid bridge structure between particles;
fig. 4 is a three-dimensional liquid bridge structure of the top layer particles.
Detailed Description
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Referring to fig. 1, the invention provides a method for determining migration criteria of a sodium-cooled fast reactor chip bed, which combines particle density, size, shape and position to perform stress analysis on chip particles in the chip bed, introduces liquid bridge force representing the action of liquid surface tension, and according to practical situations, the chip particles of the chip bed may form liquid bridges with a plurality of chip particles contacted with the periphery of the chip particles at the same time, so as to obtain liquid bridge force combining force at the bottom of the chip particles formed by the combined action of the liquid bridge force, obtain a vertical stress balance equation born by the chip particles in the chip bed in a critical state in the migration process, obtain relative speeds between the chip particles and fluid under the action of liquid surface tension, finally consider the external fluid speed, compare the relative speeds between the particles and the fluid, judge whether the chip bed has migration phenomenon, and effectively evaluate the migration characteristics of the chip bed in a lower cavity in a reactor core disassembly accident.
The invention relates to a sodium-cooled fast reactor fragment bed migration criterion method which comprises the following specific steps:
s1, calculating and analyzing the influence of external fluid applied by the fragment particles in the fragment bed and self gravity to perform stress analysis;
when the debris bed is at rest, a mechanical equilibrium equation is established, and the debris particles are affected by external fluid drag, external fluid buoyancy, the gravity of the particles themselves, and the liquid bridge force, as shown in fig. 2:
F D +F b ＝F g +F g combination
Wherein F is D For external fluid drag, F b For buoyancy of external fluid, F g For the self-gravity of the chip particles F G combination Is the liquid bridge force at the bottom of the chip particles.
External fluid drag force F experienced by the debris particles D Buoyancy F of external fluid b And the self gravity F of the particles g The calculation is as follows:
wherein C is d For drag coefficient, d is the particle diameter of the chip, ρ m Is the average density of gas-liquid two-phase flow, v' eq To take into account the relative velocity ρ between the debris particles and the fluid by the surface tension of the liquid p The chip particle density, g is the gravitational acceleration.
S2, solving the resultant force action influence of the liquid bridge force influence generated among the fragment particles in the fragment bed by analyzing the resultant force action influence of the liquid bridge force influence, and introducing the resultant force action influence into an equilibrium state equation;
due to the action of the surface tension of the liquid, liquid bridges are generated among the lyophilic fragment particles immersed in the liquid, the structure of the liquid bridges is shown in fig. 3, and along with the generation of the liquid bridges, liquid bridge force action is generated among the fragment particles, which is the external appearance of the surface tension and capillary force of the liquid bridges. Considering that the liquid bridge force applied in critical state force balance is composed of surface Zhang Lixiang and capillary pressure term, the size is related to the geometry of the liquid bridge and the wetting property of the chip particles, and is the liquid surface tension coefficient sigma T Is a function of (2).
In contrast to the static liquid bridging force between every two fragment particles, the fragment particles in the fragment bed may form liquid bridges with several fragment particles in contact with each other around them at the same time. Assuming that the chip bed particles are in a compact rhombohedral stacking mode, a liquid bridge three-dimensional model between the top chip particles and the chip particles below the top chip particles is shown in fig. 4, and the size of the liquid bridge force borne by the top chip particles in the vertical direction is the resultant action of three liquid bridges at the bottom of the top chip particles.
Specific hydraulic bridge force resultant force can be obtained:
wherein F is G 2 pi R as the liquid bridge force between the chip particles 2 σ T As a surface tension term,as capillary pressure term, sigma T Is the surface tension coefficient, ΔP is the capillary pressure difference, R 1 Is the contour radius of the liquid bridge, R 2 Is the radius of the neck of the liquid bridge.
Specifically, the liquid bridge contour radius R 1 And liquid bridge neck radius R 2 The calculation is as follows:
wherein a is the space between the particles of the fragments, d is the diameter of the particles of the fragments, θ c For the contact angle of the debris particles with the liquid, δ is the liquid filling angle between the particles and a schematic diagram of the relationship between these parameters is given in fig. 3.
And S3, solving an equilibrium state equation to obtain the relative speed between the fragment particles and the fluid, thereby obtaining the interphase equilibrium speed of the liquid bridge force.
By passing throughThe formulas in S1 and S2 are combined to obtain the relative velocity v 'between the debris particles and the fluid considering the action of the surface tension of the liquid' eq ：
Wherein ρ is p Is particle density ρ m Is the average density of gas-liquid two-phase flow, g is gravity acceleration, d is particle diameter, C d For drag coefficient, sigma T R is the surface tension coefficient 1 Is the contour radius of the liquid bridge, R 2 Is the radius of the neck of the liquid bridge.
S4, comparing the external fluid velocity with the relative velocity between the fragment particles and the fluid by solving the external fluid velocity, and judging whether migration occurs.
The calculation of the flow rate of the fluid outside the chip particles (mainly referred to as gas in the experiment) is obtained in the experiment by a calculation formula of the evaporation rate of the coolant in the simultaneous chip bed and the equivalent decay heat power of the chip particles. For the bottom gas injection experiments of the present invention, the gas velocity outside the chip particles can be directly obtained by the gas injection flow rate and the gas flow area between the chip particles.
Fluid flow velocity v g The calculation is as follows:
wherein Q is the gas injection flow rate, A is the fragment bed cross-sectional area, α g Epsilon is the porosity of the fragment bed, which is the flow cross-section average void fraction.
α g For the average cavitation fraction of the flow cross section, the value is difficult to determine by experimental measurement. To reduce potential simulation errors and expand the applicability of the model, the following expression is used:
wherein alpha is gExp For the volume average void fraction of the fluid in the chip bed,and (3) correcting the coefficient for the section cavitation share, and fitting the coefficient by experimental data.
Due to the flow resistance of the debris particles, during the dynamic process of gas injection, most of the stored gas is present inside the debris bed, alpha gExp The calculation formula of (2) is as follows, and meanwhile, the simplification treatment is carried out by considering that the bottom section area of the experimental tank in the experimental process is fixed and unchanged:
wherein DeltaV is the variation of the fluid volume, V p For the total volume of the chip bed portion, Δh is the variation value of the liquid level, h p Epsilon is the porosity of the bed of fragments, which is the average height of the bed of fragments.
And comparing the relative speed between the particles and the fluid obtained in the step S3 with the flow speed of the fluid to judge whether the migration of the fragment bed occurs or not.
Wherein v is g For external fluid flow velocity, v' eq Is the relative velocity between the particles and the fluid.
The debris bed particles remain stationary when the relative velocity between the debris bed particles and the fluid is greater than or equal to the fluid flow rate, and migration of the debris bed occurs only when the relative velocity between the debris particles and the fluid is less than the fluid flow rate.
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In order to verify the correctness and effectiveness of the sodium-cooled fast reactor fragment bed migration method, a fragment bed bottom nitrogen injection experiment is adopted for verification, fourteen groups of typical migration experiment working conditions are selected for simulation, and the following detailed experiment parameter list and calculation results of fourteen groups of working conditions are as follows:
table 1 results of migration criteria model simulation before and after improvement
V obtained by simulation calculation g And v' eq The difference value can reflect the inclination angle of the fragment bed to a certain extent from the migration critical state in the experimental process, thereby further proving the rationality of the improved migration criterion method. In general, by introducing a liquid bridge force model representing the action of the surface tension of liquid, the prediction accuracy of the model on the migration behavior of small-size particles is effectively improved, and the simulation range of the model is expanded.
In summary, the invention provides a method for determining migration criteria of a sodium-cooled fast reactor fragment bed, which combines particle density, size, shape and position to perform stress analysis on fragment particles in the fragment bed, introduces a resultant force of liquid bridge force representing the action of liquid surface tension to obtain a stress balance equation in a critical state in the migration process, obtains the relative speed between the fragment particles and fluid under the action of the liquid surface tension, compares the relative speed between the fragment particles and the fluid with the external fluid speed in consideration of the external fluid speed, judges whether the fragment bed has migration phenomenon, effectively evaluates the migration characteristics of the fragment bed in a lower cavity in a reactor core disassembly accident of the sodium-cooled fast reactor, and correctly predicts the movement trend of the fragment bed in the migration process.
The above is only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited by this, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (5)
1. A migration criterion method of a sodium-cooled fast reactor fragment bed is characterized in that stress analysis is carried out on fragment particles in the fragment bed by combining the density, the size, the shape and the position of the particles, meanwhile, liquid bridge force representing the action of liquid surface tension is introduced, according to practical conditions, the fragment particles of the fragment bed form liquid bridges with a plurality of fragment particles in contact with the periphery of the fragment particles at the same time, liquid bridge force combining force at the bottom of the fragment particles formed by the combined action of the liquid bridge force is obtained, a vertical stress balance equation born by the fragment particles in the fragment bed in a critical state in the migration process is obtained, the relative speed between the fragment particles with the action of the liquid surface tension and fluid is obtained, and finally, the external fluid speed is considered, so that whether the migration phenomenon of the fragment bed occurs is judged; the criteria are as follows:
wherein v is g For external fluid flow velocity, v e ′ q To take into account the relative velocity between the debris particles and the fluid due to the surface tension of the liquid;
the vertical force balance equation borne by the chip particles in the chip bed is as follows:
F D +F b ＝F g +F g combination
Wherein F is D For external fluid drag, F b For buoyancy of external fluid, F g For the self-gravity of the chip particles F G combination The liquid bridge force at the bottom of the chip particles is applied;
liquid bridge force F at bottom of chip particle G combination The calculation is as follows:
wherein F is G 2 pi R as the liquid bridge force between the chip particles 2 σ T As a surface tension term,as capillary pressure term, sigma T Is the surface tension coefficient, ΔP is the capillary pressure difference, R 1 Is the contour radius of the liquid bridge, R 2 Is the radius of the neck of the liquid bridge;
liquid bridge contour radius R 1 And liquid bridge neck radius R 2 The calculation is as follows:
wherein a is the space between the particles of the fragments, d is the diameter of the particles of the fragments, θ c The contact angle between the chip particles and the liquid is shown, and delta is the liquid filling angle between the particles;
relative velocity v 'between the debris particles and the fluid taking into account the effect of the surface tension of the liquid' eq The calculation is as follows:
wherein sigma T R is the surface tension coefficient 1 Is the contour radius of the liquid bridge, R 2 Is the radius of the neck of the liquid bridge.
2. According to the weightsThe method for determining migration criteria of sodium-cooled fast reactor chip bed of claim 1, wherein the chip particles are subjected to an external fluid drag force F D Buoyancy F of external fluid b And the self gravity F of the chip particles g The calculation is as follows:
wherein C is d For drag coefficient, d is the particle diameter of the chip, ρ m Is the average density of gas-liquid two-phase flow, v' eq To take into account the relative velocity ρ between the debris particles and the fluid by the surface tension of the liquid p The chip particle density, g is the gravitational acceleration.
3. The method for determining migration criteria of sodium-cooled fast reactor chip bed according to claim 1, wherein the external fluid velocity v g The calculation is as follows:
wherein Q is the gas injection flow rate, A is the fragment bed cross-sectional area, α g Epsilon is the porosity of the fragment bed, which is the flow cross-section average void fraction.
4. A sodium-cooled fast reactor chip bed migration criterion method according to claim 3, characterized in that the flow cross-section average void fraction α g The calculation is as follows:
α g ＝α gExp C αg
wherein alpha is gExp A volume average void fraction of fluid within the debris bed;and obtaining the value of the section void fraction correction coefficient by obtaining the average void fraction and the minimum or maximum effective void fraction of each group volume through experimental measurement for the section void fraction correction coefficient.
5. The method of claim 4, wherein the volume average void fraction α of the fluid in the debris bed is gExp The calculation is as follows:
wherein DeltaV is the variation of the fluid volume, V p For the total volume of the chip bed portion, Δh is the variation value of the liquid level, h p Epsilon is the porosity of the bed of fragments, which is the average height of the bed of fragments.
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