A prediction method for tangential fretting in liquid lead-bismuth alloy environment

Abstract

The present invention proposes a method for predicting tangential micro-motion wear in a liquid lead-bismuth alloy environment, which relates to the field of nuclear energy industry technology. The flow distribution in the fuel rod bundle structure is obtained through CFD analysis, sub-channel program analysis or experimental measurement, and then converted into a force function that varies with time and position as input for fluid-solid coupling calculation; the vibration response of the flow-induced vibration is obtained through fluid-solid coupling, and the parameters are extracted. The vibration response parameters are brought into the working rate calculation formula to obtain the micro-motion wear working rate; the micro-motion wear coefficient is obtained according to the experimental results; the micro-motion wear volume rate is obtained based on the established micro-motion wear calculation method, and the wear depth is obtained according to the wear depth calculation method; the maximum wear depth is used to predict whether the fuel rod cladding meets the mechanical integrity requirements. The present invention establishes a prediction model for tangential micro-motion wear in a liquid lead-bismuth alloy environment, which provides a reference for fuel assembly safety analysis and design.

Description

Technical Field

[0001] The present invention relates to the technical field of nuclear energy industry, and in particular to a method for predicting tangential fretting wear in a liquid lead-bismuth alloy environment. Background Art

[0002] In order to meet the development goals of economic efficiency, safety and sustainability of nuclear energy systems, the International Forum on the Fourth Generation Nuclear Energy System has selected six reactor types with the greatest development potential, including lead-based cold reactors, to form the fourth-generation reactor system. Due to the low melting point and high boiling point of lead-based materials, the reactor can also obtain high outlet temperature when operating at low pressure, avoiding the loss of coolant accidents caused by high-pressure systems, and achieving high thermoelectric conversion efficiency. In addition, lead-based materials have high chemical stability and weak reactivity with air and water. Compared with sodium-cooled reactors, they can avoid safety issues such as fire and explosion. At the same time, lead-based materials have strong heat carrying capacity and natural circulation capacity, and can rely on natural circulation to discharge residual heat from the core. The core of the lead-based fast reactor uses box-type components that do not require refueling, and the refueling cycle is more than 20 years. It has a high degree of inherent safety and passive safety, which is conducive to preventing nuclear proliferation and has a very good development prospect.

[0003] However, during the actual operation of the reactor, the coolant continuously flushes the fuel assembly, and the fuel rods are disturbed by it and vibrate slightly, which is the flow-induced vibration phenomenon. This slight vibration will cause slight friction, impact and other interactions between structural components, thereby causing damage to the material, which is fretting. Therefore, based on the fretting abrasion characteristics of wire-wound positioning fuel rods and assemblies in a lead-bismuth environment, the present invention establishes a coupling method of fretting abrasion and flow-induced vibration, and further provides a tangential fretting abrasion prediction method in a liquid lead-bismuth alloy environment, providing a reference for fuel assembly safety analysis and design. Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting tangential micro-abrasion in a liquid lead-bismuth alloy environment, which can propose corresponding solutions to the problems existing in the prior art and provide a reference for the safety analysis and design of fuel assemblies.

[0005] The embodiment of the present invention is achieved as follows:

[0006] The embodiment of the present application provides a method for predicting tangential fretting wear in a liquid lead-bismuth alloy environment, which is characterized by comprising the following steps:

[0007] Step 1: Obtain the flow distribution in the fuel bundle structure through CFD analysis, sub-channel program analysis or experimental measurement, and further obtain the power spectrum density PSD of the turbulent excitation force, which is then converted into a force function that varies with time and position as input for structural response;

[0008] Step 2: Obtain the vibration response of flow-induced vibration through fluid-solid coupling, extract parameters such as vibration amplitude, main vibration frequency, natural frequency, etc., bring the vibration response parameters into the working rate calculation formula, and calculate the corresponding fretting abrasion working rate;

[0009] Step 3: Obtain the fretting wear coefficient based on the existing experimental results;

[0010] Step 4: Obtain the fretting abrasion volume rate based on the established fretting abrasion calculation method, and obtain the abrasion depth according to the abrasion depth calculation model;

[0011] Step 5: Analyze the abrasion depth.

[0012] In some embodiments of the present invention, the working rate calculation formula in step 2 above is:

[0013]

[0014] where y max is the maximum vibration displacement, in m; f is the natural frequency in the worst case, in 1 / s; m is the mass per unit length, in kg / s; l is the span of the beam, in m; ζ s is the damping ratio, which is a constant; μ is the friction coefficient, which is a constant; working rate It is the power generated by the abrasion of the entire system, measured in W.

[0015] In some embodiments of the present invention, the fretting erosion calculation method in step 2 above is:

[0016]

[0017] Where K is the fretting wear coefficient.

[0018] In some embodiments of the present invention, when the micro-friction characteristic region is in the initial running-in region and the rising region, the friction coefficient μ is in the range of 0-0.6, when the micro-friction characteristic region is in the descending region, the friction coefficient μ is in the range of 0.4-0.6, and when the micro-friction characteristic region is in the stable region, the friction coefficient μ is in the range of 0.3-0.4.

[0019] In some embodiments of the present invention, the abrasion depth calculation model in step 4 above is:

[0020]

[0021] In some embodiments of the present invention, the abrasion depth obtained in step 4 is corrected according to the following calculation method:

[0022]

[0023] Where t is time.

[0024] In some embodiments of the present invention, the reference method for predicting whether the fuel rod cladding meets the mechanical integrity requirements in the above step 5 is that when the abrasion depth is less than one tenth of the thickness of the fuel rod cladding, the mechanical integrity requirements are met, and when the abrasion depth is not less than one tenth of the thickness of the fuel rod cladding, the mechanical integrity requirements are not met.

[0025] Compared with the prior art, the embodiments of the present invention have at least the following advantages or beneficial effects:

[0026] The present invention provides a method for predicting tangential fretting corrosion in a liquid lead-bismuth alloy environment, fully considering the corrosion characteristics of lead-bismuth alloy, and establishing a theoretical prediction model for fretting corrosion of fuel rods for wire winding positioning of lead-bismuth fast reactor fuel assemblies. The calculation results of the method for predicting tangential fretting corrosion in a liquid lead-bismuth alloy environment more realistically reflect the damage of the fuel rod cladding, providing a reference for the safety analysis and design of fuel assemblies. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0028] Figure 1 A flow chart of fretting calculation and analysis provided in an embodiment of the present invention;

[0029] Figure 2 It is a three-dimensional diagram of the fretting friction characteristics under different displacement amplitudes in the prior art;

[0030] Figure 3 It is a micro-motion diagram of micro-motion operation condition in the prior art;

[0031] Figure 4 A cross-sectional schematic diagram of contact abrasion between a cylinder and a plane provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0033] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0034] In actual situations, flow-induced vibration is caused by the work done by the exciting force on the structure. The energy absorbed by the structure will be dissipated in a variety of damping methods, including inherent structural damping, additional mass force damping generated by the fluid, friction damping, nonlinear contact damping, etc. When the inherent structural damping and additional mass force damping cannot dissipate the energy absorbed by the structure, the excess energy will be dissipated by doing work on other structures, including friction work, nonlinear collision, etc., which is the root cause of the abrasion phenomenon. Therefore, how to accurately estimate the work done by the structure on the external structure is the key to studying abrasion behavior.

[0035] like Figure 1 The steps include:

[0036] Step 1: Obtain the flow distribution in the fuel bundle structure through CFD analysis, sub-channel program analysis or experimental measurement, and further obtain the power spectrum density PSD of the turbulent excitation force, which is then converted into a force function that varies with time and position as input for structural response;

[0037] Step 2: Obtain the vibration response of flow-induced vibration through fluid-solid coupling, extract parameters such as vibration amplitude, main vibration frequency, natural frequency, etc., bring the vibration response parameters into the working rate calculation formula, and calculate the corresponding fretting abrasion working rate;

[0038] Step 3: Obtain the fretting wear coefficient based on the existing experimental results;

[0039] Step 4: Obtain the fretting abrasion volume rate based on the established fretting abrasion calculation method, and obtain the abrasion depth according to the abrasion depth calculation model;

[0040] Step 5: Compare the maximum corrosion depth with relevant criteria and establish a corrosion prediction method to predict whether the fuel rod cladding meets the mechanical integrity requirements.

[0041] Theoretical calculation method:

[0042] The realization of theoretical calculation mainly lies in estimating the energy absorbed by the structure from the work done by the exciting force and calculating the work done by the structure to the outside.

[0043] The energy absorption power calculation formula of the fuel rod can estimate the energy absorbed by the fuel rod in the process of turbulent excitation force doing work. Formula 1 is as follows:

[0044]

[0045] Among them, S FF is the power spectral density (PSD) of the fuel rod vibration, f n is the frequency of vibration represented by the external force function, and M is the mass of the excited object. In reality, the flow-induced vibration of the fuel rod often has the maximum amplitude at the natural frequency of the system, so considering the calculation margin and envelope, f n Set as the natural frequency of the system. Smith modified the energy absorption formula to Formula 2 based on the mode of the fuel rod under unit beam span and mass:

[0046]

[0047] S ff The natural frequency of the i-th mode under the unit beam span is f i The PSD of the local force, is the joint acceptance of the i-th mode. The Smith modified formula takes into account the energy absorption rate of the fuel rod in different modes. However, since the PSD in different modes needs to be considered in Formula 2, this will greatly increase the workload of evaluating the abrasion results caused by flow-induced vibration, which is not conducive to engineering applications. Therefore, a method that can quickly calculate PSD is needed.

[0048] The general relationship for the vibration response of a beam to random excitation is given by Equation 3 and Equation 4:

[0049]

[0050]

[0051] RMSdisplacement is the root mean square displacement of the continuous beam rod bundle caused by flow, where L is the tube length, M is the mass of the tube, and f 1 is the natural frequency of the tube, ω 1 is the natural cyclic frequency of the tube, ξ is the damping ratio, f is the vibration frequency, is the effective tube length involving spatial correlation, <p(t) 2 >′ is the root mean square value of the exciting force per unit time.

[0052] The random excitation vibration displacement relationship is modified and simplified to obtain a new relationship between the beam span and amplitude, which is as follows:

[0053]

[0054] y in formula 5 2 (x) is the root mean square value of the tube vibration amplitude, S Fis the PSD of the pipe vibration derived from the random vibration theory, ξ is the damping ratio, C 1 is the vibration point correction coefficient at different positions in the unit beam span. For the sake of conservatism, the present invention takes the C of the maximum amplitude point as 1 The correction is 0.4213 (x = 0.581L), where L is the span of the beam. After considering different modes and simplifying, the following formula 6 can be obtained:

[0055]

[0056] Where ζ i is the damping ratio of the i-th mode, which is a constant, Y rms 2 is RMSdisplacement, i.e. the root mean square value of the pipe vibration. Combining formula 2 and formula 5, we can get the following formula 7:

[0057]

[0058] Through the above transformation, the relationship between the energy absorption of the tube and the root mean square amplitude and frequency is established, which avoids the direct use of vibration parameters of different modes for calculation, and can achieve rapid evaluation of energy absorption. It can be obtained from the above formula that the energy absorbed by the tube in flow-induced vibration is related to the vibration frequency of the tube, the root mean square value of the amplitude, the damping ratio and the unit mass of the beam. Taking into account the convenience and conservatism of the evaluation, the present invention still uses the natural frequency as the calculation frequency in the formula. It should be noted that this is the energy absorbed by the tube in only one vibration direction. Usually, the tube vibrates in orthogonal directions, which means that the tube simultaneously absorbs the energy generated by the work done by the exciting force in the orthogonal direction. Therefore, for a straight tube, the total power absorbed is twice that of Formula 7, that is, the following Formula 8:

[0059]

[0060] Among them, P Totol is the total absorbed power per unit span of the beam, in W; m is the mass per unit length of the rod, in kg / m; L is the span length of the beam, in m; f iRefers to the i-th order natural frequency, unit is Hz, Yrms2 refers to the maximum root mean square vibration value, unit is m. It can be reasonably assumed that the main vibration frequency of the tube with the same parameters of the support with gap and the ideal support is similar, so it can be concluded that the energy absorption of the two is also similar. Next, a conservative assumption is made, assuming that the energy absorbed by the tube is only dissipated by viscous damping and friction damping in the shear direction, and the shear power on the boundary is defined here. The definition of shear power is similar to that of vibration absorption power. It is assumed that the shear force is the same as the normal force in the orthogonal direction. Using the shear force instead of the normal force in the orthogonal direction can obtain the dissipated power of the shear force work, and it is assumed that the dissipated power is the power dissipated by friction damping. Therefore, the shear work rate is obtained The formula 9 is as follows:

[0061]

[0062] Equation 9 gives the parameters that affect the turbulence-induced energy absorption mechanism. As mentioned earlier, the accepted practice in fretting erosion prediction is to use a normalized work rate of Instead of shear work rate. In actual situations, the standard work rate can be expressed by shear power and friction coefficient μ, as formula 10:

[0063]

[0064] The general working rate prediction formula is as follows:

[0065]

[0066] In formula 11, A is the correction factor for different support structures, such as support gap and support type (i.e., drilled holes, lattice bars, pull holes, etc.) and its gap / preload conditions. This factor is generally measured experimentally.

[0067] In actual situations, fuel rods that experience flow-induced vibrations often have gaps with the support constraint structure, so it is necessary to further modify the working rate prediction formula under ideal support conditions. In the prior art, Yetisir et al. found based on experimental results that when the gap between the support and the tube is 20% of the maximum gap, the impact on the vibration response is the greatest. After exceeding 20% ​​of the maximum gap, the vibration response will decrease with the increase of the gap, and finally stabilize in the 50% to 100% area of ​​the maximum gap. Based on the above existing research results, a new working rate prediction standard is proposed after modifying the formula (Formula 11). The standard is based on parameters such as vibration frequency, vibration amplitude at the mid-span position, beam span, tube mass and empirical abrasion coefficient. This criterion uses linear vibration analysis (i.e., the vibration frequency caused by turbulence and the vibration amplitude caused by the mid-span). This standard can be used to quickly evaluate the working rate, and then quickly evaluate the abrasion damage of fuel rods caused by flow-induced vibration. All parameters used are obtained by widely generalized parameter research conducted by nonlinear finite element programs. Working rate The calculation standard is as follows: Formula 12:

[0068]

[0069] where y max is the maximum vibration displacement, in m; f is the natural frequency in the worst case, in 1 / s; m is the mass per unit length, in kg / s; l is the span of the beam, in m; ζ s is the damping ratio, which is a constant; μ is the friction coefficient, which is a constant; working rate It is the power generated by the abrasion of the entire system, measured in W.

[0070] The vibration root mean square at the maximum displacement in the formula should be noted as follows: ① All current methods for calculating the abrasion working rate are derived and calculated based on the root mean square value of the flow-induced vibration amplitude; ② The flow-induced vibration is a random vibration and the vibration amplitude at different positions also has certain differences. Therefore, the root mean square value of the vibration amplitude will have a certain range of variation. In order to ensure that the micro-motion abrasion volume calculation has sufficient conservatism and envelope, the present invention will select the maximum value of the vibration root mean square value for calculation; ③ In order to ensure the conservatism of the micro-motion abrasion calculation, the common international practice is that it is believed that the vibration amplitude will eventually be converted into the sliding distance between the fuel rod and the contact object. Therefore, it is in line with international practice to use the maximum value of the root mean square value of the vibration amplitude as the calculation parameter of the working rate.

[0071] In the formula (Formula 12), ζ sis the damping ratio of the pipe. This parameter is related to the inherent damping and vibration characteristics of the system and can only be obtained based on experimental measurements and empirical calculations. In the prior art, an empirical relationship for calculating the damping ratio in flow-induced vibrations is proposed based on experimental verification. It is believed that the essence of damping is to dissipate the kinetic energy of vibration, and the kinetic energy of vibration is positively correlated with the frequency of vibration. Therefore, damping is related to the frequency of vibration. The empirical relationship for calculating the damping ratio is as follows: Formula 13:

[0072]

[0073] Where f is the frequency of the tube vibration. The damping ratio calculated by this formula meets the parameter requirements of formula 12.

[0074] From formula 12 and formula 13, we can get the maximum vibration root mean square y max , the natural frequency f in the most extreme case, the span l of the beam, the damping ratio ζ s The friction coefficient μ can be used to obtain the fretting working rate under specific vibration conditions through theoretical calculation. The first four parameters can be obtained through numerical calculation and analysis of flow-induced vibration.

[0075] In the theoretical formula, the friction coefficient will directly affect the calculation of the working rate. However, during the micro-motion process, the friction coefficient is often not a constant, so the change process of the friction coefficient needs to be analyzed.

[0076] Based on a large number of tangential fretting experimental studies, three basic types of Ft-D curves have been obtained, including linear, elliptical and parallelogram types, which can cover the most basic and important information of fretting wear. According to the dynamic change of the Ft-D curve with the number of fretting cycles (N), the Ft-DN fretting friction characteristic curve can be obtained. The three-dimensional diagram of the fretting friction characteristics under different displacement amplitudes (Ft-DN three-dimensional diagram) is shown in the figure. Figure 2 As shown, Figure 2 Selected from the literature [Zhou Zhongrong, Vincent L. Fretting [M]. Shanghai: Shanghai Jiaotong University Press, 2004], where a is a linear friction characteristic curve, b is an elliptical characteristic curve, and c is a parallelogram friction characteristic curve. Figure 2 The fretting friction area in a is also called the partial slip zone. Figure 2 The micro-friction area in b is also called the mixing area. Figure 2 The micro-friction area in middle c is also called the complete slip zone.

[0077] The friction coefficient will directly affect the calculation of the working rate, and the friction coefficient is often not a constant during the micro-motion process, so it is necessary to analyze the change process of the friction coefficient. In the process of micro-motion abrasion, the friction coefficient is not constant, and there are multiple processes in the process of micro-motion abrasion:

[0078] 1. In the initial stage of fretting, the fuel rod is in the local slip zone. At this stage, the fretting mainly acts on the oxide layer on the surface of the fuel rod. The core area of ​​the contact surface is also in an adhesive state, accompanied by the generation of a small amount of abrasive debris.

[0079] 2. In the transition stage of fretting, as the fretting process deepens, the fretting displacement amplitude gradually increases, and the fretting friction characteristics gradually change to mixed zone characteristics. In this process, the core area of ​​the contact surface also begins to slide relative to each other, abrasive debris begins to be generated rapidly, and the friction coefficient also begins to increase rapidly;

[0080] 3. In the stable stage of fretting, when the generation and adhesion of abrasive debris tend to be stable, abrasive grooves and abrasive pits begin to appear, and the fretting friction characteristics are transformed into the slip zone. At this stage, the interaction between the contact surfaces manifests itself as a complete slip state, and the friction coefficient gradually decreases from the highest point and eventually tends to be stable, and fretting will also occur rapidly.

[0081] According to the above micro-motion friction characteristics, the micro-motion diagram of the motion condition can be obtained. Figure 3 As shown, selected from [Zhang Xiaoyu. Research on the tangential micro-motion wear mechanism of nuclear power steam generator heat transfer tubes [D]; Southwest Jiaotong University, 2009]. According to the prior art, an experimental study on the micro-motion wear characteristics at room temperature was carried out based on the I-800 alloy. The experimental results show that the friction coefficient increases first, then decreases, and finally stabilizes with the increase of the number of cycles. Combined with the prior art, a study on the micro-motion wear characteristics of the pressurized water reactor steam generator heat transfer tube was carried out based on the I-600 alloy. In this study, it was found that higher ambient temperature will cause the friction coefficient to decrease to a certain extent. As the micro-motion wear time increases, the change trend of the friction coefficient is divided into: rapid increase, decrease after reaching the highest point, and finally stabilized. As the temperature increases, the friction coefficient gradually decreases, and the abrasion volume also decreases with the increase of time.

[0082] In summary, when the fretting friction characteristic area is in the initial running-in area and the rising area, the friction coefficient ranges from 0 to 0.6; when the fretting friction characteristic area is in the descending area, the friction coefficient ranges from 0.4 to 0.6; when the fretting friction characteristic area is in the stable area, the friction coefficient ranges from 0.3 to 0.4.

[0083] The abrasion coefficient needs to be obtained through experimental measurement. The measurement method is in the prior art, so it will not be described in detail here. At the same time, there are also representative abrasion experiments in the prior art.

[0084] The theoretical calculation model of the abrasion depth of fuel rod cladding is as follows:

[0085] The cladding abrasion is estimated by calculating the abrasion amount based on the combined state of the abrasion scars. Figure 4Cross-sectional view of the abrasion caused by contact between a cylinder and a flat surface.

[0086] The cross-sectional area A of the eroded cladding can be expressed as:

[0087]

[0088] By series expansion, we can get:

[0089]

[0090]

[0091]

[0092] It can be deduced that:

[0093]

[0094]

[0095] Where D = 2R.

[0096] If L represents the abrasion width (along the axial direction of the fuel rod), the abraded volume is:

[0097]

[0098] So the abrasion depth h is expressed as:

[0099]

[0100] Assuming that the abrasion width is equal to the width of the grid rigid convexity, for a given abrasion amount, there is a certain abrasion depth. The cladding abrasion depth is determined by the following formula:

[0101]

[0102] The maximum abrasion depth is compared with relevant criteria to determine whether the fuel rod cladding meets the mechanical integrity requirements. Generally, relevant engineering criteria require that the maximum abrasion depth is less than 10% of the cladding thickness.

[0103] Since LBE is more corrosive than Pb in a high temperature environment, the abrasive volume in a liquid Pb environment will be smaller than that in a liquid LBE environment under the same working conditions. Therefore, this study needs to further correct the results obtained in a liquid Pb environment to ensure that the results of the theoretical calculation are sufficiently conservative.

[0104] According to the experimental results of the prior art "Study on the Corrosion Behavior of T91 and 316L Steel in LBE", the oxidation corrosion of liquid LBE on both stainless steels is significantly stronger than that on liquid Pb. The depth of oxidation corrosion gradually decreases with the appearance of the oxide layer. According to the experimental results, after 1000 hours of corrosion, the oxide layer thickness of 316L stainless steel in LBE is 0.16μm thicker than that in liquid Pb. This study linearly processed the corrosion depth over time and believed that in the absence of an oxide layer, 316L stainless steel forms an oxide layer of 0.0016μm more per hour in LBE than in Pb.

[0105] Since the theoretical calculation formula of the present invention is derived based on the abrasion test data in the Pb environment, and the corrosion behavior itself has no direct relationship with the fretting corrosion. Therefore, it can be considered that the corrosion effect has a significant effect on the abrasion coefficient K and the working rate. The influence of is very limited, so the theoretical calculation results can be corrected to obtain a more accurate abrasion volume under LBE environment. The calculation method is: the abrasion volume rate is calculated using the abrasion calculation formula of this study After that, the abrasion depth h is calculated using formula 14 and formula 15, and then the abrasion depth h is corrected to obtain the abrasion depth per unit time considering the corrosion effect. Then the corresponding abrasion volume rate is obtained The calculation method is as follows:

[0106]

[0107] The t in the formula is time, and the unit is h. The abrasion depth per unit time is calculated After substituting back to formula 14, the abrasion volume rate considering LBE corrosion can be obtained:

[0108] According to the above calculation method, a rapid evaluation of the micro-motion abrasion results in the liquid LBE environment can be achieved, and the abrasion characteristics such as the abrasion volume rate and abrasion depth under the condition of LBE oxidation corrosion can be obtained, and then the influence of the micro-motion abrasion caused by the flow-induced vibration of the fuel rod on the fuel rod cladding can be evaluated, providing a reference for reactor safety and design.

[0109] Example 1

[0110] Analysis of single rod abrasion characteristics

[0111] This embodiment uses Fluent fluid-solid coupling calculation to perform numerical calculation of flow-induced vibration on a wire-wound single rod. The calculated vibration response characteristics can be directly connected to the abrasion calculation program. After calculation by the abrasion calculation program, the abrasion result can be quickly obtained. The parameters of the wire-wound single rod and the flow-induced vibration response parameters are shown in the following table:

[0112] Table 1. Parameters of single wire-wound rod and flow-induced vibration response parameters

[0113]

[0114] The vibration displacements in Table 1 are the root mean square values ​​of the vibration amplitudes at the maximum displacement point at the center of a single rod.

[0115] The numerical calculation results are input into the abrasion calculation program, and the calculation results are shown in the following table:

[0116] Table 2. Calculation results of abrasion of a single wire-wound rod

[0117]

[0118]

[0119] According to the calculated abrasion volume rate, the abrasion volume after the set abrasion time is quickly estimated. The abrasion volume after 150h abrasion is shown in the following table:

[0120] Table 3. Theoretical calculation results of 150h wear volume

[0121]

[0122] As shown in Table 3, the theoretical calculation results of the fretting erosion caused by the flow-induced vibration of the wire-wound single rod are close to the experimental results of Karlsruhe Institute of Technology in Germany, and the theoretical calculation results have good credibility.

[0123] According to the calculation results of micro-motion wear, the wear volume of 150h is: 0.00041~0.0028mm3. The corresponding wear depth calculated by formula (Formula 15) is: 1.6422×10-5~5.9091×10-5mm. After considering the corrosion effect of LBE, the wear depth is further corrected. The wear depth calculated by formula 16 is: 4.0422×10-5~8.3091×10-5mm. Based on the cladding thickness of 0.57mm for standard fuel rods, the proportion of the wear depth of 150h to the cladding thickness is: 0.0071~0.0146%.

[0124] According to the above results, it can be seen that the vibration frequency of the wire-wound single rod is low and has high damping, so the vibration amplitude is at a low level, and the resulting micro-motion abrasion effect is also very limited. On the contrary, the corrosion effect of LBE contributes more to the abrasion depth in the entire micro-motion abrasion process. Therefore, according to the flow-induced vibration characteristics of the wire-wound single rod, the corrosion effect of LBE should be given more attention than the abrasion effect caused by micro-motion. Even though LBE is highly corrosive, according to the correction results of the micro-motion abrasion depth, it can still be seen that the abrasion depth of the wire-wound single rod after 150h of micro-motion abrasion caused by flow-induced vibration does not exceed 10% of the cladding thickness. According to the design criteria for nuclear power plant fuel assemblies, its micro-motion abrasion results are acceptable.

[0125] Example 2

[0126] Analysis of Rod Bundle Abrasion Characteristics

[0127] This embodiment conducts fretting erosion characteristic analysis based on the numerical calculation results of flow-induced vibration of the wire-wound rod bundle. Considering that the fretting erosion of the rod bundle will eventually be reflected in the fretting erosion between the fuel rods and the grid in the rod bundle, this embodiment first analyzes the flow-induced vibration characteristics of the wire-wound rod bundle, selects representative fuel rods, analyzes their flow-induced vibration characteristics, and brings their natural frequency, vibration frequency, damping ratio, vibration amplitude and other parameters into the fretting erosion calculation program, thereby realizing the rapid calculation and evaluation of the fretting erosion results of the wire-wound rod bundle. The numerical calculation results of the wire-wound rod bundle are shown in Table 4.

[0128] Table 4. Parameters of wire rod bundle and flow-induced vibration response parameters

[0129]

[0130] The fixing methods of the wire rod bundles in Table 4 are all fixed at the lower end and fixed at the upper end. From the parameters in Table 4, it can be seen that the response characteristics of the flow-induced vibration of the wire rod bundles with different diameters are somewhat different. The natural frequency of the wire rod bundle with a wire diameter of 2.0 mm is larger, and the vibration frequency is also larger, which means that the vibration damping ratio will be reduced to a certain extent; the vibration displacement of the wire rod bundle with a wire diameter of 1.9 mm is significantly larger than that of the single wire rod. According to the above characteristics, the fretting erosion result will be significantly increased. The fretting erosion calculation results are shown in Table 5.

[0131] Table 5. Calculation results of fretting wear of wire rod bundle

[0132]

[0133] According to the calculated abrasion volume rate, the abrasion volume after the set abrasion time is quickly estimated. The abrasion volume after 150h abrasion is shown in the following table:

[0134] Table 6. Theoretical calculation results of 150h wear volume

[0135]

[0136] According to the calculation results of micro-motion abrasion, the abrasion volume of the 1.9mm diameter fuel rod after 150h micro-motion abrasion is: 0.0028~0.0072mm3, and the corresponding abrasion depth calculated by formula 15 is: 5.9090×10-5~1.1091×10-4mm. After considering the corrosion effect of LBE, the abrasion depth is further corrected, and the abrasion depth is calculated by formula 16 to be: 8.3090×10-5~1.3491×10-4mm. Based on the cladding thickness of 0.57mm for standard fuel rods, the proportion of the abrasion depth of 150h to the cladding thickness is: 0.0146~0.0237%.

[0137] The abrasion volume of a 2.0mm wire diameter fuel rod after 150h of micro-abrasion is 0.0440~0.1150mm3. The corresponding abrasion depth calculated by formula 15 is 3.7072×10-4~7.0341×10-4mm. After further correction of the abrasion depth considering the corrosion effect of LBE, the abrasion depth calculated by formula 16 is 3.9472×10-4~7.2741×10-4mm. Based on the cladding thickness of 0.57mm for standard fuel rods, the proportion of the abrasion depth of 150h to the cladding thickness is 0.0650~0.1276%.

[0138] The calculation results show that, in the process of fretting, the contribution of LBE corrosion effect to fretting is less than that of fretting induced by flow-induced vibration, relative to the higher level of flow-induced vibration response. For fretting induced by flow-induced vibration, the natural frequency of the rod bundle with a winding diameter of 2 mm is greatly increased due to its winding characteristics. The increase in the natural frequency leads to a higher frequency of the main vibration frequency of the rod bundle. According to formula 12, the contribution of the main vibration frequency to the working rate is significantly higher than that of the amplitude, damping and other parameters, which leads to the working rate of the fuel rod with a winding diameter of 2 mm being in a very high range during the fretting process. This is determined by the vibration characteristics themselves, which will result in a more serious fretting result. For the wire-wound rod bundle with a wire diameter of 1.9 mm, according to the numerical calculation results of flow-induced vibration, it can be seen that the natural frequency of the 1.9 mm wire-wound rod bundle is 12.128 Hz, which is close to the natural frequency of the single wire-wound rod, so its main vibration frequency will also be at a lower level. Even if its vibration amplitude is much larger than that of the wire-wound rod bundle with a wire diameter of 2 mm, the contribution of the amplitude to the micro-motion abrasion working rate is smaller than that of the main vibration frequency. Therefore, the micro-motion abrasion depth of the wire-wound rod bundle with a wire diameter of 1.9 mm is much smaller than that of the wire-wound rod bundle with a wire diameter of 2 mm.

[0139] From the above analysis, it can be concluded that the vibration frequency of the fuel rod is more important for the fretting erosion. In the process of suppressing the fretting erosion of the fuel rod, reducing the main vibration frequency of the fuel rod by adjusting the constraint conditions can better avoid the more serious erosion consequences in the fretting erosion process induced by flow-induced vibration.

[0140] In summary, the embodiments of the present invention provide a method for predicting tangential micro-abrasion in a liquid lead-bismuth alloy environment, which fully considers the corrosion characteristics of lead-bismuth alloy, and establishes a theoretical prediction model for micro-abrasion of fuel rods for wire winding positioning of lead-bismuth fast reactor fuel assemblies. The calculation results of the method for predicting tangential micro-abrasion in a liquid lead-bismuth alloy environment more realistically reflect the damage of the fuel rod cladding, provide a reference for the safety analysis and design of fuel assemblies, and lay the foundation for further optimization of the prediction model later.

[0141] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting tangential fretting wear in a liquid lead-bismuth alloy environment, characterized in that: The steps include: Step 1: Obtain the flow distribution in the fuel bundle structure through CFD analysis, sub-channel program analysis or experimental measurement, and further obtain the power spectrum density PSD of the turbulent excitation force, which is then converted into a force function that varies with time and position as input for structural response; Step 2: Obtain the vibration response of flow-induced vibration through fluid-solid coupling, extract the parameters of vibration amplitude, main vibration frequency, and natural frequency, substitute the vibration response parameters into the working rate calculation formula, and calculate the corresponding fretting abrasion working rate; Step 3: Obtain the fretting wear coefficient based on the existing experimental results; Step 4: Obtain the fretting abrasion volume rate based on the established fretting abrasion calculation method, and obtain the abrasion depth according to the abrasion depth calculation model; Step 5: Analyze the abrasion depth; The working rate calculation formula in step 2 is where y max is the maximum vibration displacement, in m; f is the worst-case natural frequency in 1 / s; m is the mass per unit length in kg / s; l is the span of the beam in m; ζ s is the damping ratio, which is a constant; μ is the friction coefficient, which is a constant; working rate is the power generated by the abrasion of the entire system, in W; The fretting erosion calculation method in step 2 is: Where K is the fretting wear coefficient; The calculation model of abrasion depth in step 4 is: After obtaining the abrasion depth in step 4, make corrections according to the following calculation method: Where t is time.

2. The method for predicting tangential fretting wear in a liquid lead-bismuth alloy environment according to claim 1, characterized in that: When the micro-friction characteristic area is in the initial running-in area and the rising area, the friction coefficient μ ranges from 0 to 0.6; when the micro-friction characteristic area is in the descending area, the friction coefficient μ ranges from 0.4 to 0.6; when the micro-friction characteristic area is in the stable area, the friction coefficient μ ranges from 0.3 to 0.

4.

3. The method for predicting tangential fretting wear in a liquid lead-bismuth alloy environment according to claim 1, characterized in that: The reference method for predicting whether the fuel rod cladding meets the mechanical integrity requirements in step 5 is that when the abrasion depth is less than one tenth of the thickness of the fuel rod cladding, the mechanical integrity requirements are met, and when the abrasion depth is not less than one tenth of the thickness of the fuel rod cladding, the mechanical integrity requirements are not met.

Images