An analysis method for quantitative evaluation of lead bismuth fuel leakage

Abstract

The application discloses an analysis method for quantitative evaluation of lead-bismuth fuel leakage, and steps are as follows: 1, performing lead-bismuth reactor fuel performance analysis; 2, collecting required evaluation lead-bismuth reactor operation parameter data as fuel performance analysis program input; 3, performing iterative calculation in the fuel performance analysis program until the result converges, obtaining output results such as fission gas release type and share; 4, according to the specific design of the required evaluation lead-bismuth reactor, selecting fuel rods and coolant regions for modeling and simplification; 5, in the ANSYS Fluent of the CFD software, adopting the VOF method, combining the material transport model and the k-epsilon turbulence model, taking the output results in step 3 as conditions, giving the lead-bismuth reactor leakage fission gas source term and boundary conditions in the model built in step 4, simulating the distribution and leakage behavior characteristics of the fission gas when the lead-bismuth reactor fuel rod cladding is damaged, and performing quantitative evaluation. The application provides theoretical support for evaluating the leakage characteristics of the lead-bismuth reactor, fills the gap in the field, and has important significance for safety analysis.

Description

Technical Field

[0001] This invention belongs to the field of two-phase flow numerical simulation technology, specifically relating to an analytical method for quantitative assessment of lead-bismuth fuel leakage based on a lead-bismuth fuel performance analysis program and the commercial CFD software Fluent. Background Technology

[0002] Lead-cooled fast reactors, which use lead-based materials as coolants, are one of the six main types of fourth-generation nuclear power reactors. A lead-cooled fast reactor refers to a fast neutron reactor cooled by liquid lead or a lead-bismuth alloy. It primarily focuses on lead-bismuth reactors cooled by lead-bismuth alloys. These reactors generally employ a closed fuel cycle and possess excellent nuclear waste transmutation and fuel breeding capabilities. Due to their superior economic advantages, thermal performance, and safety, they have become a major research target for countries worldwide.

[0003] However, due to the unique properties of lead-bismuth reactors, such as deeper burn-up, more severe corrosion of the cladding by lead and bismuth, higher cladding temperature, larger temperature gradient, greater fission gas release, and higher internal pressure, the possibility of cladding failure in lead-bismuth reactors is also increased. In response to the current development and design requirements of lead-bismuth reactors, developing new in-core behavior and failure performance analysis programs for lead-bismuth reactor fuel elements, especially in-core performance analysis programs for MOX fuel elements, has become a key research area for many countries worldwide in promoting the development of lead-cooled fast reactors. New theoretical calculation results and computational simulation tools are constantly being generated and optimized in this process; however, a complete and comprehensive research method for fission gas leakage in lead-bismuth reactors is still lacking. Summary of the Invention

[0004] To overcome the problems existing in the prior art, the present invention aims to provide an analytical method for quantitative assessment of lead-bismuth fuel leakage based on a lead-bismuth fuel performance analysis program and the commercial CFD software Fluent. This invention focuses on lead-bismuth reactors, analyzing lead-bismuth fuel elements, identifying fission product source terms in the lead-bismuth reactor, and then conducting relevant numerical simulation studies on the fission product distribution and leakage behavior characteristics based on the Fluent CFD software. This provides theoretical support for assessing the leakage characteristics of lead-bismuth reactors, fills a gap in this field, and is of significant importance for their safety analysis.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] An analytical method for quantitative assessment of lead-bismuth fuel leakage is proposed. Based on the study of the behavior of lead-bismuth reactor fuel elements, such as pore migration model, cesium migration model, and cladding corrosion model, the fuel performance of lead-bismuth reactor is analyzed to obtain the source terms of fission products of lead-bismuth reactor. Then, based on the commercial CFD program Fluent, relevant numerical simulation studies are carried out on the distribution of fission products and leakage behavior characteristics.

[0007] The method includes the following steps:

[0008] An analytical method for quantitative assessment of lead-bismuth fuel leakage, comprising the following steps:

[0009] Step 1: Based on the study of lead-bismuth reactor fuel element behavior, considering the pore migration model, cesium migration model and cladding corrosion model, conduct fuel performance analysis of lead-bismuth reactor;

[0010] For the pore migration model, under fast reactor conditions, i.e., when the linear heat generation rate (LHGR) and local fuel burnup exceed 30 kW / m and 100 MWd / kgHM respectively, a physical phenomenon of fuel structure reorganization is expected to occur, leading to fuel pore migration and subsequent central void formation. The pore redistribution is controlled by the following kinetic equation (1):

[0011]

[0012] In formula (1):

[0013] P – Fuel porosity / %;

[0014] v p — Pore migration velocity / m·s -1 ;

[0015] r—radius / m;

[0016] t — migration time / s;

[0017] For the cesium migration model, the cesium migration process is controlled by the following equation (2):

[0018]

[0019] In formula (2):

[0020] C cs —Cesium concentration, atoms / m 3 ;

[0021] J cs —Cesium flux, atoms / m 2 / s;

[0022] Y cs —Cesium fission yield: ~20%;

[0023] F — fission rate density, fission / m 3 / s;

[0024] For the cladding corrosion model, a Fe3O4 layer will form on the surface of the lead coolant in the stainless steel cladding. The internal spinel layer does not come into contact with the lead coolant. At this stage, the growth of the spinel layer follows the parabolic law. As the spinel layer grows, its thickness will gradually reach a critical thickness. At this thickness, the diffusion rate of Fe through the spinel layer and the disappearance rate of Fe caused by the flow of lead coolant are equal. After this, the lead coolant begins to come into contact with the internal spinel layer and corrosion begins.

[0025] When HT-9 is selected as the cladding material, the corrected corrosion coefficient k p The relation is given by the following equation (3):

[0026] In formula (3):

[0027] k p0 —Initial corrosion coefficient = 9.735 × 10 -8 ;

[0028] C0 — Mass concentration of the corrosive solution (ppm);

[0029] Q—Heat of reaction / kJ / mol;

[0030] R = 8.314 J / mol / K;

[0031] T—Clad temperature / K;

[0032] Step 2: Collect the necessary data on lead-bismuth reactor operating parameters for evaluation, and use them as input for the fuel performance analysis program;

[0033] Step 3: Perform iterative calculations in the fuel performance analysis program until the results converge, and obtain the output results of the types and proportions of fission gas released;

[0034] The thermal calculation section consists of modules such as fuel and cladding temperature model, fuel and cladding deformation model, internal pressure model, fission gas release model, cladding high-temperature oxidation model, and cladding bubbling failure model.

[0035] Step 4: Based on the specific design of the lead-bismuth reactor to be evaluated, select the fuel rod and coolant regions for modeling and simplify the model and mesh generation;

[0036] Step 5: In the CFD software ANSYS Fluent, the VOF method is used, combined with the mass transport model and the k-ε turbulence model. Using the output results in Step 3 as conditions, the lead-bismuth reactor leakage fission gas source terms and boundary conditions are given in the model established in Step 4. The lead-bismuth eutectic alloy parameters are imported into Fluent in the form of UDF to simulate the distribution and leakage behavior characteristics of fission gas when the fuel rod cladding of the lead-bismuth reactor is damaged, and a quantitative evaluation is performed.

[0037] This analytical method has the following advantages:

[0038] 1. This invention proposes a complete set of analytical methods for quantitative assessment of lead-bismuth fuel leakage, filling a gap in this field, providing theoretical support for assessing the leakage characteristics of lead-bismuth piles, and having significant implications for their safety analysis;

[0039] 2. During fuel performance analysis, after coupling the physical model applicable to fast reactors with the original analysis program, subsequent modifications to the relevant formulas and materials in the model are only required for different types of fast reactors, without needing to modify the entire program, thus saving time.

[0040] 3. The analytical method for quantitative assessment of lead-bismuth fuel leakage can save a lot of experimental time and resources, which is of great significance to the development of lead-bismuth reactors. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0042] Figure 2 This is a flowchart of the calculation process in the lead-bismuth fuel performance analysis program.

[0043] Figure 3 This is a simplified model of the shell-break-coolant channel in the example. Detailed Implementation

[0044] The present invention will be further described below with reference to examples and accompanying drawings:

[0045] like Figure 1 As shown, this invention provides an analytical method for quantitative assessment of lead-bismuth fuel leakage. Taking the analysis of a 1mm diameter breakage in the cladding of a 10MW small natural circulation lead-cooled fast reactor core at the end of its life cycle as an example, the method includes the following steps:

[0046] Step 1: Based on the study of lead-bismuth reactor fuel element behavior, considering pore migration model, cesium migration model, cladding corrosion model, etc., conduct lead-bismuth reactor fuel performance analysis.

[0047] For the pore migration model, under fast reactor conditions, i.e., when the linear heat generation rate (LHGR) and local fuel burnup exceed 30 kW / m and 100 MWd / kgHM respectively, the physical phenomenon of fuel structure reorganization is expected to occur, leading to fuel pore migration and subsequent central void formation. Pore redistribution can be controlled by the following kinetic equation (1):

[0048]

[0049] In formula (1):

[0050] P – Fuel porosity / %;

[0051] v p — Pore migration velocity / m·s -1 r — radius / m;

[0052] t — migration time / s;

[0053] For cesium migration models, under typical light water reactor conditions, the cesium concentration is relatively low and the fuel burnup is also relatively low, so its migration behavior exhibits some inertia. Furthermore, the fuel temperature of LWRs is insufficient to trigger the cesium migration process. However, in the design of lead-bismuth reactors, due to their special conditions of high temperature and high burnup, the cesium migration behavior can no longer be ignored. The cesium migration process can be controlled by the following equation (2):

[0054]

[0055] In formula (2):

[0056] C cs —Cesium concentration, atoms / m 3 ;

[0057] J cs —Cesium flux, atoms / m 2 / s;

[0058] Y cs —Cesium fission yield: ~20%;

[0059] F . — Fission rate density, fission / m 3 / s.

[0060] For the cladding corrosion model, a Fe3O4 layer forms on the surface of the lead coolant in the stainless steel cladding. The internal spinel layer does not come into contact with the lead coolant. At this stage, the growth of the spinel layer follows the parabolic law. As the spinel layer grows, its thickness gradually reaches a critical thickness. At this thickness, the diffusion rate of Fe through the spinel layer and the disappearance rate of Fe caused by the flow of lead coolant are equal. After this, the lead coolant begins to contact the internal spinel layer and corrosion begins.

[0061] When HT-9 is selected as the cladding material, the corrected corrosion coefficient k p The relation is given by the following equation (3):

[0062] In formula (3):

[0063] k p0 —Initial corrosion coefficient = 9.735 × 10 -8 ;

[0064] C0 — Mass concentration of the corrosive solution (ppm);

[0065] Q—Heat of reaction / kJ / mol;

[0066] R = 8.314 J / mol / K;

[0067] T – cladding temperature / K.

[0068] Step 2: Input the operating parameter data of the 10MW small natural circulation lead-cooled fast reactor as the fuel performance analysis program.

[0069] Step 3: Perform iterative calculations in the fuel performance analysis program until the results converge, and obtain the output results such as the types and proportions of fission gases released in the 10MW small natural circulation lead-cooled fast reactor at the end of the core phase.

[0070] The thermal calculation section mainly consists of modules such as fuel and cladding temperature models, fuel and cladding deformation models, internal pressure models, fission gas release models, cladding high-temperature oxidation models, and cladding bubbling failure models. After step 1, the physical models suitable for lead-bismuth reactors, namely the pore migration model, cesium migration model, and cladding corrosion model, are coupled in and can be used for lead-bismuth fuel performance analysis. Iterative calculations are then performed based on the fuel performance analysis program input from step 2, such as... Figure 2 As shown, this yields output results such as the types and proportions of fission gas released.

[0071] Step 4: Based on the specific design of the 10MW small natural circulation lead-cooled fast reactor, select a suitable location for modeling. To simplify the model, this example selects the extraction test rod and the adjacent coolant channel for modeling, such as... Figure 3 As shown, the left side represents the experimental rod, and the right side represents the adjacent coolant channel; the two parts are connected by a 1mm diameter slit. The most crucial aspect of this step is model simplification and mesh generation, which directly impacts the computational quality and speed of step 5. After simplification comparison verification and mesh independence verification, selecting a simpler model with fewer meshes and higher quality will significantly save computational resources and improve computational convergence.

[0072] Step 5: In the commercial CFD software ANSYS Fluent, the VOF (volume function of fluid) method is used, combined with the mass transport model and the k-ε turbulence model. Using the output results in Step 3 as conditions, the source terms and boundary conditions of the lead-bismuth reactor leakage fission gas are given in the model established in Step 4. The lead-bismuth eutectic alloy parameters are imported into Fluent in the form of UDF to simulate the distribution and leakage behavior characteristics of fission gas when the fuel rod cladding of the lead-bismuth reactor is damaged, and a quantitative evaluation is performed.

[0073] All contents not described in detail in this invention are common knowledge in the field.

Claims

1. An analytical method for quantitative assessment of lead-bismuth fuel leakage, characterized in that: The method includes the following steps: Step 1: Based on the study of lead-bismuth reactor fuel element behavior, considering the pore migration model, cesium migration model and cladding corrosion model, conduct fuel performance analysis of lead-bismuth reactor; For the pore migration model, under fast reactor conditions, i.e., when the linear heat generation rate (LHGR) and local fuel burnup exceed 30 kW / m and 100 MWd / kgHM respectively, a physical phenomenon of fuel structure reorganization is expected to occur, leading to fuel pore migration and subsequent central void formation. The pore redistribution is controlled by the following kinetic equation (1): In formula (1): P – Fuel porosity / %; v p — Pore migration velocity / m·s -1 ; r—radius / m; t — migration time / s; For the cesium migration model, the cesium migration process is controlled by the following equation (2): In formula (2): C cs —Cesium concentration, atoms / m 3 ; J cs —Cesium flux, atoms / m 2 / s; Y cs —Cesium fission yield / 20%; — Fission rate density, fission / m 3 / s; For the cladding corrosion model, a Fe3O4 layer will form on the surface of the lead coolant in the stainless steel cladding. The internal spinel layer does not come into contact with the lead coolant. At this stage, the growth of the spinel layer follows the parabolic law. As the spinel layer grows, its thickness will gradually reach a critical thickness. At this thickness, the diffusion rate of Fe through the spinel layer and the disappearance rate of Fe caused by the flow of lead coolant are equal. After this, the lead coolant begins to come into contact with the internal spinel layer and corrosion begins. When HT-9 is selected as the cladding material, the corrected corrosion coefficient k p The relation is given by the following equation (3): In formula (3): k p0 —Initial corrosion coefficient = 9.735 × 10 -8 ; C0 — Mass concentration of the corrosive solution (ppm); Q—Heat of reaction / kJ / mol; R = 8.314 J / mol / K; T—Clad temperature / K; Step 2: Collect the necessary data on lead-bismuth reactor operating parameters for evaluation, and use them as input for the fuel performance analysis program; Step 3: Perform iterative calculations in the fuel performance analysis program until the results converge, and obtain the output results of the types and proportions of fission gas released; The thermal calculation section consists of modules such as fuel and cladding temperature model, fuel and cladding deformation model, internal pressure model, fission gas release model, cladding high-temperature oxidation model, and cladding bubbling failure model. Step 4: Based on the specific design of the lead-bismuth reactor to be evaluated, select the fuel rod and coolant regions for modeling and simplify the model and mesh generation; Step 5: In the CFD software ANSYS Fluent, the VOF method is used, combined with the mass transport model and the k-ε turbulence model. Using the output results in Step 3 as conditions, the lead-bismuth reactor leakage fission gas source terms and boundary conditions are given in the model established in Step 4. The lead-bismuth eutectic alloy parameters are imported into Fluent in the form of UDF to simulate the distribution and leakage behavior characteristics of fission gas when the fuel rod cladding of the lead-bismuth reactor is damaged, and a quantitative evaluation is performed.

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