Method for analyzing vibration wear of lead-based reactor wire winding positioning fuel assembly

Abstract

The invention provides an analysis method for vibration wear of a lead-based reactor winding wire positioning fuel assembly, and belongs to the technical field of lead-based fast reactor fuel analys.The analysis method comprises the steps that the normal load between a fuel rod and a winding wire winding the fuel rod, the sliding distance and the stress of the winding wire are obtained; and determining the wear depth of the cladding of the fuel rod according to the normal load, the slippage distance and the stress of the winding wire. The fuel rod cladding wear depth is detected through a numerical simulation method, the blank of a reactor core fuel assembly vibration wear numerical analysis method is filled up, a fuel assembly vibration wear preliminary research means is provided for the initial stage of fast reactor core design, the uncertainty during fast reactor research design and safety analysis is solved, and the method is suitable for mass production. And the research and design efficiency of the lead-based fast reactor core is improved.

Description

Technical Field

[0001] This invention relates to the field of lead-based fast reactor fuel analysis technology, and in particular to an analysis method for vibration wear of lead-based reactor wire-wound positioning fuel assemblies. Background Technology

[0002] Due to the unique nature of radioactivity, the primary prerequisite for the large-scale use of nuclear energy is ensuring that radioactive materials do not leak. Nuclear fuel is the main source of radioactivity in a reactor. To prevent radioactive release, the fuel rods in the reactor are surrounded by a metal cladding. Therefore, ensuring the integrity of the cladding structure is a necessary prerequisite for preventing radioactive release.

[0003] Lead-based fast reactor core fuel rods are typically wound with metal wires. These wires not only secure and space the fuel rods but also enhance coolant mixing within the channels, thereby improving heat transfer. As burnup progresses, vibrational wear occurs between the metal wires and the fuel rod cladding. Excessive wear on the fuel rod cladding can lead to radioactive release. Therefore, accurately detecting the wear depth of the fuel rod cladding is crucial for preventing radioactive release. Summary of the Invention

[0004] This invention provides an analytical method for vibration wear of lead-based reactor wire-wound positioning fuel assemblies, in order to solve the technical problem of how to detect the wear depth of fuel rod cladding.

[0005] This invention provides a method for analyzing the vibration and wear of wire-wound positioning fuel assemblies in lead-based reactors, comprising: Obtain the normal load, slip distance, and force on the winding wire between the fuel rod and the winding wire. The wear depth of the fuel rod cladding is determined based on the normal load, the slip distance, and the force on the winding wire.

[0006] According to the present invention, a method for analyzing the vibration wear of wire-wound fuel assemblies in lead-based reactors includes determining the wear depth of the fuel rod cladding based on the normal load, the slip distance, and the force on the wire, comprising: The minor and major axes of the contact ellipse between the casing and the winding wire are determined based on the force applied to the winding wire. The wear depth is determined based on the normal load, the slip distance, the minor axis, and the major axis.

[0007] According to the present invention, a method for analyzing vibration wear of wire-wound positioning fuel assemblies in lead-based reactors includes determining the minor and major axes of the contact ellipse between the cladding and the wire based on the forces acting on the wire, comprising: The half-width of the contact ellipse is determined based on the force applied to the winding wire; The minor axis is determined based on the half-width; The long axis is indeed determined based on the short axis.

[0008] According to the present invention, an analysis method for vibration wear of wire-wound positioning fuel assemblies in lead-based reactors is provided, wherein determining the half-width of the contact ellipse based on the force on the wire includes: Obtain the axial length of the winding, the radius of the winding, the radius of the fuel rod, the Young's modulus of the cladding, the Poisson's ratio of the cladding, the Young's modulus of the winding, and the Poisson's ratio of the winding; The equivalent elastic modulus is determined based on the Young's modulus of the casing, the Poisson's ratio of the casing, the Young's modulus of the winding, and the Poisson's ratio of the winding. The half-width is determined based on the force applied to the winding, the axial length of the winding, the radius of the winding, the radius of the fuel rod, and the equivalent elastic modulus.

[0009] According to the present invention, a method for analyzing vibration wear of a lead-based reactor wire-wound positioning fuel assembly is provided, wherein determining the short axis based on the half-width includes: The short axis is obtained by doubling the half-width.

[0010] According to the present invention, a method for analyzing vibration wear of a lead-based reactor wire-wound positioning fuel assembly is provided, wherein determining the long axis based on the short axis includes: Obtain the radius of the fuel rod, the pitch of the winding wire, the radius of the winding wire, and the angle between the winding wire and the axis of the fuel rod; The maximum radius of curvature of the winding is determined based on the radius of the fuel rod and the pitch of the winding. The major axis is determined based on the minor axis, the maximum radius of curvature, the radius of the fuel rod, the radius of the winding wire, and the included angle.

[0011] According to the present invention, a method for analyzing vibration wear of wire-wound positioning fuel assemblies in lead-based reactors, wherein determining the wear depth based on the normal load, the slip distance, the minor axis, and the major axis includes: The wear coefficient between the casing and the winding wire, the material hardness of the casing and the winding wire, and the radius of the fuel rod are obtained. The wear depth is determined based on the wear coefficient, the normal load, the slip distance, the minor axis, the major axis, the material hardness, and the radius of the fuel rod.

[0012] According to the present invention, a method for analyzing the vibration wear of wire-wound fuel assemblies in lead-based reactors, after determining the wear depth of the fuel rod cladding based on the normal load, the slip distance, and the force on the wire, further includes: If the ratio of the wear depth to the thickness of the casing is a preset value, the wear life of the fuel rod is determined based on the force on the winding wire and the slip distance.

[0013] According to the present invention, a method for analyzing the vibration wear of wire-wound fuel assemblies in lead-based reactors is provided, wherein determining the wear life of the fuel rod based on the force on the wire and the slippage distance includes: The minor and major axes of the contact ellipse between the casing and the winding wire are determined based on the force applied to the winding wire. The wear life is determined based on the short axis, the long axis, and the slip distance.

[0014] According to the present invention, a method for analyzing vibration wear of wire-wound positioning fuel assemblies in lead-based reactors, wherein determining the wear life based on the minor axis, the major axis, and the slip distance includes: Obtain the radius and vibration period of the fuel rod, and the wear volume of the fuel rod within a single vibration period; The wear life is determined based on the thickness of the casing, the short axis, the long axis, the radius of the fuel rod, the slip distance, the vibration period, and the wear volume.

[0015] This invention provides an analysis method for vibration wear of lead-based reactor filament-wound fuel assemblies. Based on the normal load between the fuel rod and the filament, the slip distance, and the force on the filament, the method determines the cladding wear depth of the fuel rod. This is equivalent to detecting the cladding wear depth of the fuel rod through numerical simulation, filling a gap in numerical analysis methods for core fuel assembly vibration wear. It provides a means for preliminary research on fuel assembly vibration wear in the early stages of fast reactor core design, resolves uncertainties in fast reactor research and design as well as safety analysis, and improves the efficiency of lead-based fast reactor core research and design. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0017] Figure 1 This is one of the flowcharts illustrating the analysis method for vibration wear of lead-based reactor wire-wound positioning fuel assemblies provided by the present invention.

[0018] Figure 2 This is a schematic diagram of the structure of the fuel rod and the winding wire provided by the present invention.

[0019] Figure 3 This is a schematic diagram of the contact ellipse between the fuel rod and the winding wire provided by the present invention.

[0020] Figure 4 This is the second flowchart illustrating the analysis method for vibration wear of lead-based reactor wire-wound positioning fuel assemblies provided by this invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0022] Generally, liquid lead / lead alloy coolants have high density and high flow velocity, leading to vibration-like failure phenomena in densely packed fuel rod bundles within the reactor core. As burnup intensifies, pellet swelling and cladding thermal expansion reduce the gap between the coils and adjacent fuel rods, sometimes even causing contact. The high-density coolant scouring the fuel rod bundles exerts a significant additional effect, inducing vibration. Simultaneously, the positioning coils disturb the boundary layer, causing intense turbulent mixing, flow sweeping, and transverse flow. The axial and circumferential anisotropy of the fuel assembly flow field becomes more pronounced, and high turbulent kinetic energy and strong pressure pulses further exacerbate fuel rod vibration. High-frequency, high-amplitude vibration of the fuel rods can lead to fatigue damage. The cutting and impact between the coils and adjacent rods wears away the oxide layer, accelerating cladding erosion and increasing the risk of fuel element damage and leakage, threatening the integrity of the reactor's first boundary and safe reactor operation.

[0023] In the field of reactor core vibration damage analysis, existing technologies mainly focus on the vibration wear of traditional fuel rods and positioning grids in water reactors, while research on the vibration wear of wire-wound fuel assemblies in fast reactors is severely lacking. Furthermore, existing technologies for analyzing fuel rod vibration wear primarily employ experimental methods. While the experimental results are reliable, they are challenging, time-consuming, and costly, making it difficult to conduct preliminary analysis of reactor core fuel rod damage issues in the early stages of reactor design.

[0024] The following is combined Figures 1-4 This invention describes an analytical method for vibration wear of wire-wound positioning fuel assemblies in lead-based reactors.

[0025] Figure 1This is one of the flowcharts illustrating an analytical method for vibration wear of lead-based reactor wire-wound positioning fuel assemblies provided by the present invention. Figure 1 As shown, including but not limited to the following steps: Step S1: Obtain the normal load, slip distance, and force on the winding between the fuel rod and the winding that winds around the fuel rod.

[0026] The structure of fuel rod 10 and wire winding 20 is as follows Figure 2 As shown. Normal load F1 is the normal force between the wire and the fuel rod, in N (Newtons). Slip distance L1 is the cumulative distance of relative sliding between the wire and the fuel rod, in meters (m). Force F2 on the wire is the force applied to the wire, in N.

[0027] Step S2: Determine the wear depth of the fuel rod cladding based on the normal load, slip distance, and the force on the winding wire.

[0028] In one embodiment, step S2 may further include: The minor and major axes of the contact ellipse between the cladding and the winding are determined based on the forces acting on the winding. The wear depth is determined based on the normal load, slip distance, and minor and major axes. The contact ellipse between the shell and the winding is as follows: Figure 3 As shown, a is the major axis and b is the minor axis.

[0029] In one embodiment, the present invention determines the minor and major axes of the contact ellipse between the sheath and the winding wire based on the force applied to the winding wire, and may further include: The half-width of the contact ellipse is determined based on the force applied to the winding wire. Determine the minor axis based on the half-width; The short axis is indeed the long axis.

[0030] In one embodiment, the invention determines the half-width of the contact ellipse based on the force applied to the wound wire, which may further include: Obtain the axial length of the winding, the radius of the winding, the radius of the fuel rod, the Young's modulus of the cladding, the Poisson's ratio of the cladding, the Young's modulus of the winding, and the Poisson's ratio of the winding. The equivalent elastic modulus is determined based on the Young's modulus of the casing, the Poisson's ratio of the casing, the Young's modulus of the winding, and the Poisson's ratio of the winding. The half-width is determined based on the force on the winding, the axial length of the winding, the radius of the winding, the radius of the fuel rod, and the equivalent elastic modulus.

[0031] The axial length L2 of the winding is the total length of the winding along the axial direction of the fuel rod, in meters (m). The radius r of the winding and the radius R of the fuel rod are both in meters. The Young's modulus of the cladding... Young's modulus of the wound wire The unit for all of them is Pa (Pa).

[0032] Among them, equivalent elastic modulus The calculation formula is: ; The Poisson's ratio of the shell, The Poisson's ratio for the wound silk.

[0033] Based on Hertz contact theory, the formula for calculating the half-width c is: ; In one embodiment, the invention, which determines the minor axis based on half-width, may further include: Doubling the half-width gives the minor axis, i.e., minor axis b = 2c; In one embodiment, the invention, which determines the major axis based on the minor axis, may further include: Obtain the radius of the fuel rod, the pitch of the winding, the radius of the winding, and the angle between the winding and the axis of the fuel rod; The maximum radius of curvature of the winding is determined based on the radius of the fuel rod and the pitch of the winding. The major axis is determined based on the minor axis, the maximum radius of curvature, the radius of the fuel rod, the radius of the winding wire, and the included angle.

[0034] This invention assumes that both the wire winding and the fuel rod cladding material are 316L stainless steel. The wire winding pitch H1 is the distance traveled along the axial direction of the fuel rod in one winding revolution, measured in meters (m). Figure 3 As shown, the angle between the winding wire and the fuel rod axis is... ; The unit of the maximum radius of curvature R1 is m, and the formula for calculating R1 is: ; Suppose we have parameters A and B, and A and B satisfy the following relationship: ; ; Where R2=+ ; A and B can be determined based on the two relationships between A and B.

[0035] The formula for calculating the major axis 'a' is: ; In one embodiment, the invention determines the wear depth based on the normal load, slip distance, minor axis, and major axis, and may further include: Obtain the wear coefficient between the cladding and the winding, the material hardness of the cladding and the winding, and the radius of the fuel rod; The wear depth is determined based on the wear coefficient, normal load, slip distance, minor axis, major axis, material hardness, and fuel rod radius.

[0036] The wear coefficient k is in mm. 3 / m, the unit of material hardness H2 is MPa.

[0037] Assuming the wear between the casing and the winding is represented by a cylinder with an elliptical base, then according to the Archard wear formula: ; V represents the wear volume between the casing and the wire winding, in meters (m). 3 .

[0038] In reality, the wear morphology of the wire in contact with the fuel rod consists of two quarter ellipsoids, plus a geometric body with a semi-elliptical cross-section rotated around the fuel rod axis, satisfying the following: ; Where h is the wear depth, in meters (m).

[0039] therefore We can obtain: ; Understandably, for a given fuel rod and winding wire, most parameters in this formula are constants and are eventually converted into numerical values. The variables are generally only the normal load F1, the slip distance L1, and the force F2 on the winding wire.

[0040] As described above, the vibration wear analysis method of this invention determines the cladding wear depth of the fuel rod based on the normal load, slip distance, and force on the cladding between the fuel rod and the filament. This is equivalent to detecting the cladding wear depth of the fuel rod through numerical simulation. Specifically, starting from the vibration displacement of the flow-induced vibration of the fuel rod in the reactor core, and through reasonable assumptions, combined with Hertz contact theory and wear-related theories, a simulation method is proposed for the geometric parameters of the contact area between the filament and the fuel rod, as well as parameters such as vibration wear volume and wear depth. This fills the gap in numerical analysis methods for vibration wear of reactor core fuel assemblies, provides a means for preliminary research on the vibration wear of fuel assemblies in the early stages of fast reactor core design, solves the uncertainties in fast reactor research and design and safety analysis, and improves the efficiency of lead-based fast reactor core research and design.

[0041] In one embodiment, such as Figure 4 As shown, after step S2, the method for analyzing vibration wear of lead-based reactor wire-wound positioning fuel assemblies of the present invention may further include: Step S3: If the ratio of wear depth to shell thickness is a preset value, the wear life of the fuel rod is determined based on the force and slippage distance of the winding.

[0042] The preset value can be 10%. In engineering, it is generally considered that the wear life of a fuel rod is when the wear depth reaches 10% of the thickness of the fuel rod cladding.

[0043] In one embodiment, step S3 may further include: The minor and major axes of the contact ellipse between the cladding and the winding are determined based on the forces acting on the winding. Wear life is determined based on the short axis, long axis, and slip distance.

[0044] In one embodiment, the invention determines wear life based on the minor axis, the major axis, and the slip distance, and may further include: Obtain the radius and vibration period of the fuel rod, and the wear volume of the fuel rod within a single vibration period; Wear life is determined based on the thickness of the cladding, the minor axis, the major axis, the radius of the fuel rod, the slip distance, the vibration period, and the wear volume.

[0045] The vibration period T0 is measured in seconds (s), and the wear volume V of the fuel rod during a single vibration period is... T0 The unit is m 3 The thickness of the casing The unit is m, and the unit of wear life t is days.

[0046] The formula for calculating wear life t can be: ; Thus, the present invention can further determine the wear life of fuel rods based on the wear depth.

[0047] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of analyzing wire-wound position fuel assembly vibration wear in a lead-based reactor, characterized by, The method comprises: obtaining a normal load, a slip distance and a stress of a wire wound around a fuel rod between the fuel rod and the wire; determining an abrasion depth of a cladding of the fuel rod according to the normal load, the slip distance and the stress of the wire.

2. The method of claim 1, wherein the method further comprises: The determining the abrasion depth of the cladding of the fuel rod according to the normal load, the slip distance and the stress of the wire comprises: determining a minor axis and a major axis of a contact ellipse between the cladding and the wire according to the stress of the wire; determining the abrasion depth according to the normal load, the slip distance, the minor axis and the major axis.

3. The method of claim 2, wherein the wire-wrapped fuel assembly vibration wear analysis of a lead-based reactor is performed by: The determining the minor axis and the major axis of the contact ellipse between the cladding and the wire according to the stress of the wire comprises: determining a half-width of the contact ellipse according to the stress of the wire; determining the minor axis according to the half-width; determining the major axis according to the minor axis.

4. The method of claim 3, wherein the wire-wrapped fuel assembly vibration wear analysis of a lead-based reactor is performed by: The determining the half-width of the contact ellipse according to the stress of the wire comprises: obtaining an axial length of the wire, a radius of the wire, a radius of the fuel rod, a Young's modulus of the cladding, a Poisson's ratio of the cladding, a Young's modulus of the wire and a Poisson's ratio of the wire; determining an equivalent elastic modulus according to the Young's modulus of the cladding, the Poisson's ratio of the cladding, the Young's modulus of the wire and the Poisson's ratio of the wire; determining the half-width according to the stress of the wire, the axial length of the wire, the radius of the wire, the radius of the fuel rod and the equivalent elastic modulus.

5. The method of claim 3, wherein the wire-wrapped fuel assembly vibration wear analysis of a lead-based reactor is performed by: The determining the minor axis according to the half-width comprises: doubling the half-width to obtain the minor axis.

6. The method of claim 3, wherein the wire-wrapped fuel assembly vibration wear analysis of a lead-based reactor is performed by: The determining the major axis according to the minor axis comprises: obtaining a radius of the fuel rod, a pitch of the wire, a radius of the wire, an included angle between the wire and an axis of the fuel rod; determining a maximum curvature radius of the wire according to the radius of the fuel rod and the pitch of the wire; determining the major axis according to the minor axis, the maximum curvature radius, the radius of the fuel rod, the radius of the wire and the included angle.

7. The method of claim 2, wherein the wire-wrapped fuel assembly vibration wear analysis of a lead-based reactor is performed by: The determining the abrasion depth according to the normal load, the slip distance, the minor axis and the major axis comprises: obtaining a wear coefficient between the cladding and the wire, material hardness of the cladding and the wire, a radius of the fuel rod; determining the abrasion depth according to the wear coefficient, the normal load, the slip distance, the minor axis, the major axis, the material hardness and the radius of the fuel rod.

8. The method of claim 1, wherein the method is used to analyze vibration wear of a lead-based reactor wire-wrapped position fuel assembly, and The method further comprises: if a ratio of the abrasion depth to a thickness of the cladding is a preset value, determining a wear life of the fuel rod according to the stress of the wire and the slip distance.

9. The method for analyzing vibration wear of lead-based reactor wire-wound positioning fuel assemblies according to claim 8, characterized in that, The determining the wear life of the fuel rod according to the stress of the wire and the slip distance comprises: determining a minor axis and a major axis of a contact ellipse between the cladding and the wire according to the stress of the wire; determining the wear life according to the minor axis, the major axis and the slip distance.

10. The method of claim 9, wherein the vibration wear of the lead-based reactor wire-wrapped position fuel assembly is analyzed by, The determining the wear life according to the short axis, the long axis and the slip distance comprises: acquiring a radius and a vibration period of the fuel rod, and a wear volume of the fuel rod in a single vibration period; determining the wear life according to the cladding thickness, the short axis, the long axis, the radius of the fuel rod, the slip distance, the vibration period and the wear volume.

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