Finite element calculation method for evaluating water erosion damage safety of steam turbine blade

Abstract

The finite element calculation method for evaluating the safety of water erosion damage of a steam turbine blade belongs to the technical field of steam turbine blades. The method solves the problem that the limit of water erosion damage of a steam turbine blade cannot be quantified in the prior art. The technical points are as follows: step 1, determining a water erosion damage area of the blade; step 2, establishing a water erosion damage model of the blade; step 3, performing finite element analysis on the water erosion damage model of the blade to determine the upper limit of the size of the water erosion damage of the blade; and step 4, evaluating the safety of the water erosion damage structure of the blade to determine the upper limit size of the damage depth and length of the blade model. The method uses three-dimensional aerodynamic flow field analysis of the blade and on-site operation records of the blade to establish a water erosion damage model of the blade, and analyzes the strength and vibration safety of the blade based on a three-dimensional finite element method to quantitatively give the limit of water erosion damage of the blade and judge the safe operation risk of the target blade, which has important guiding significance for the safe operation and precision maintenance of the blade.

Description

Technical Field

[0001] This invention relates to a calculation method for the safety of water erosion damage to turbine blades, specifically a finite element method for evaluating the safety of water erosion damage to turbine blades, belonging to the field of turbine blade technology. Background Technology

[0002] During operation, steam turbines are subjected not only to centrifugal force but also to the impact of water vapor. In the low-pressure flow path of the turbine, as the temperature and pressure parameters of the water erosion steam decrease from inlet to outlet, the water vapor undergoes a transformation from single-phase to two-phase. This causes some of the water vapor in the flow path to condense into water droplets. These droplets, mixed with high-speed water vapor, continuously impact the blades. Under the erosion of these high-speed water droplets, blade defects gradually increase until the blades break and fail. Since the working fluid of the steam turbine is water vapor, blade erosion is unavoidable. During major overhauls of steam turbine units, there is no quantitative indicator for the safety of blade water erosion damage. In most cases, whether the blades can continue to operate relies entirely on engineering experience, which introduces safety risks during blade operation. Therefore, there is an urgent need to develop a finite element method for assessing the safety of steam turbine blade water erosion damage, determining the safe operation risk of the target blade, and solving the problem of the inability to quantify the limit of blade water erosion damage. Summary of the Invention

[0003] To overcome the problem of the inability to quantify the water erosion damage limit of steam turbine blades in the prior art, this invention provides a finite element method for evaluating the safety of steam turbine blade water erosion damage. A brief overview of this invention is given below to provide a basic understanding of certain aspects of the invention. It should be understood that this overview is not an exhaustive summary of the invention. It is not intended to identify key or essential parts of the invention, nor is it intended to limit the scope of the invention.

[0004] The technical solution of the present invention:

[0005] A finite element method for evaluating the safety of turbine blades against water erosion defects includes the following steps:

[0006] Step 1: Identify the water erosion damage area on the blade.

[0007] The water erosion area can be determined by conducting a full three-dimensional aerodynamic flow field analysis of the blades, or by determining the water erosion area based on the blades' on-site operating conditions. The water erosion defect area of ​​the blades can be recorded during each major overhaul of the unit, and the severely damaged area can be identified as the water erosion defect area.

[0008] Step 2: Establish a water erosion damage model for the blades.

[0009] Based on the on-site operation and the results of the full three-dimensional aerodynamic flow field analysis, a blade water erosion defect model was established. Different depths and lengths were selected in the blade water erosion defect area to establish a combined model. The upper limit of the defect depth and length of the model is the allowable value of the blade's strength and vibration.

[0010] Step 3: Perform finite element analysis on the blade water erosion defect model to determine the upper limit of the blade water erosion defect size.

[0011] Finite element analysis includes static stress, dynamic frequency, and dynamic stress analysis;

[0012] Among them: static stress is based on finite element elastic analysis, which analyzes and evaluates the average stress and local peak stress at the critical interface of the blade;

[0013] The dynamic frequency is based on the prestress at the operating speed, and the analysis examines whether the resonant speed of the blade avoids the dangerous operating range.

[0014] Dynamic stress is based on harmonic response analysis. The pressure calculated by fluid is used as the excitation force and applied to the surface of the blade structure for response analysis. The analysis and evaluation are conducted to determine whether the dynamic stress of the blade meets the vibration resistance limit of the blade material.

[0015] Step 4: Assess the safety of the water erosion damage structure on the blade and determine the upper limit dimensions of the damage depth and length of the blade model.

[0016] Based on the finite element analysis results in step 3, the static stress water erosion defect limit, dynamic frequency water erosion defect limit, and dynamic stress water erosion defect limit of the blade are obtained. The minimum value of the water erosion defect size among the three limits is taken as the criterion for judging whether the target blade exceeds the water erosion defect size limit. If the water erosion defect of the blade exceeds this size limit, the blade will be at risk of failure; if the water erosion defect of the blade is less than this size limit, the blade can continue to operate.

[0017] Further: In step 1, a full three-dimensional aerodynamic flow field analysis of the blade is performed to obtain the streamlines and humidity of the blade under different operating conditions. Combined with the water erosion damage of the blade after actual operation of the power plant, the water erosion area of ​​the blade is determined; specifically:

[0018] First, a fluid computational geometric model of the blades is established. The model adopts a cyclic periodic symmetric model, and the geometric parameters include the mean diameter of the stationary and moving blades, blade height, root expansion angle, number of blades, and blade rotation speed.

[0019] Then, fluid meshing is performed based on the geometric model. The mesh adopts a structured hexahedral mesh, and the mesh independence is verified. The number of meshes with the optimal computational efficiency and accuracy is selected.

[0020] Then, boundary parameters were applied to the fluid mesh model. The fluid state was viscous and compressible, and the fluid satisfied the physical conservation laws. Water and water vapor were used as the working fluids. The SST turbulence model was adopted, and the wall was set as a smooth and adiabatic boundary condition. The stationary blade flow domain was set as a stationary domain, and the moving blade flow domain was set as a swirl velocity of 3000 rpm. The total pressure and total enthalpy at the flow domain inlet and the static pressure at the outlet were calculated to obtain the streamlines and humidity of the blade under different operating conditions.

[0021] Finally, based on the actual water erosion damage of the blades after the power plant's operation, the water erosion area of ​​the blades was determined. When the blades were operating at a load of over 41%, water vapor mainly eroded the inlet side of the blades. Since the airflow velocity at the tip of the blade was greater than that at the root, the inlet side of the blade tip was selected as the water erosion damage area. When the blades were operating at a load of less than 41%, water erosion occurred at the outlet side of the blade root due to eddies and backflow in the flow channel. Therefore, the outlet side of the blade root was selected as the water erosion damage area.

[0022] Further: In step 2, water erosion defect models of different heights and depths are established in the same water erosion area. For water erosion defect models in the height direction, one model is established every 50 mm; for water erosion defect models in the depth direction, one model is established every 2 mm.

[0023] Further: In step 3, finite element analysis is performed on the blade water erosion defect model. The finite element calculation model adopts a cyclic symmetric setting. The cyclic symmetric body includes a blade with one pitch and a rotor groove. Contact settings are adopted between the shrouds of the blade, between the tie rods, between the blade roots, and between the blade roots and the groove. The density, elastic modulus, and Poisson's ratio of the materials are set for the blade and the rotor. The blade and rotor mesh adopts a structured hexahedral mesh with the mesh side length ratio controlled at 3:1, and first-order reduced integral solid elements are used.

[0024] The blade static load includes centrifugal force and steam pressure. The centrifugal force is set by the rotational angular velocity of the blade and rotor, and the steam pressure is based on the fluid analysis results and is applied to the blade surface after fluid-structure interaction for static stress analysis.

[0025] The blade dynamic frequency was calculated between 2000 rpm and 3300 rpm, with dynamic frequency analysis performed every 100 rpm, and the resonant speed and resonant frequency were plotted in the Campbell diagram.

[0026] Based on the blade fluid calculation results, the blade excitation force is given through fluid-structure interaction, and the excitation factor of the excitation force is given according to the blade order and nodal diameter. Combined with the blade structure type, the damping coefficient is given, and the dynamic stress analysis of the blade is carried out using the harmonic response method.

[0027] Furthermore: In static stress analysis, when the peak stress of the blade water erosion defect model exceeds the allowable value of the blade material, the blade water erosion defect structure at this point is the upper limit size under static strength testing. The static stress testing formula for the blade is as follows:

[0028] Peak stress σ F =(σ 2 +3τ 2 ) 1 / 2 (1)

[0029] [σ]= K i / S i (2)

[0030] Peak stress σ F <[σ](3)

[0031] In the formula: σ is the principal stress; τ is the shear stress; K i S represents the yield strength of the material. i σ is the safety factor; F [σ] represents the peak stress of the blade; [σ] represents the allowable static strength of the blade.

[0032] Furthermore: In dynamic frequency analysis, when the dynamic frequency of the blade water erosion defect model exceeds the allowable safe range (operating frequency * 6% ~ operating frequency * 3%), the blade water erosion defect structure at this time is the upper limit size under the dynamic frequency test. The dynamic frequency test formula for the blade is as follows:

[0033] Bending vibration frequency

[0034] Torsional vibration frequency

[0035] Operating frequency * 6% < f 01 or f 02 <Working frequency * 3% (6)

[0036] In the formula: f 01 f is the bending vibration frequency; 02 ρ is the torsional vibration frequency; L is the blade height; A is the cross-sectional area; ρ is the blade material density; E is the material elastic modulus; G is the shear modulus; T0 is the torsional stiffness geometric factor; I0 is the polar moment of inertia of the blade section.

[0037] Furthermore: In dynamic stress analysis, when the dynamic stress of the blade water erosion defect model exceeds the allowable value of the blade material, the blade water erosion defect structure at this time is the upper limit size under the dynamic stress test. The dynamic stress test formula for the blade is as follows:

[0038]

[0039] [σa ]=σ -1 (8)

[0040]

[0041] In the formula: π is the dynamic stress of the blade; π is pi; ω is the circular frequency of vibration; δ is the attenuation rate; F M For modal forces; M M For modal mass; σ v σ is the modal stress; S is the excitation factor; β is the stress concentration factor; [σ a ] represents the allowable dynamic stress of the material; σ -1 This represents the fatigue limit of the material.

[0042] The beneficial effects of this invention are reflected in:

[0043] Compared to existing technologies, this invention employs three-dimensional aerodynamic flow field analysis of the blade and on-site blade operation records to establish a blade water erosion damage model. Based on the three-dimensional finite element method, it analyzes the blade's strength and vibration safety, quantifies the blade's water erosion damage limit, and assesses the safe operation risk of the target blade, thus solving the problem of the inability to quantify the blade's water erosion damage limit. Using this invention, long-term blade maintenance strategies can be formulated, effectively guiding power plant maintenance personnel to perform efficient maintenance, avoiding misjudgments caused by human factors, and significantly reducing the operational safety risks caused by blade water erosion damage. This invention is simple to operate, highly versatile, and can be widely applied to the safety risk assessment of turbine blade water erosion damage. This invention has significant guiding significance for the safe operation and precision maintenance of blades. Attached Figure Description

[0044] Figure 1 This is a flowchart of the finite element analysis and evaluation process for the safety of water erosion damage to blades.

[0045] Figure 2 This is a schematic diagram of the phase change of steam in the low-pressure flow path of a steam turbine;

[0046] Figure 3 It shows the fluid variation trend of the blades under different load conditions;

[0047] Figure 4 This is the result of aerodynamic flow field analysis (blade humidity cloud map);

[0048] Figure 5 The images show the water erosion conditions at the blade's operating site. Image a shows water erosion on the steam inlet side of the blade, and image b shows water erosion on the steam outlet side of the blade.

[0049] Figure 6 This is a schematic diagram of common water erosion damage on blades. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0051] Example 1, combined with Figures 1-6 This embodiment describes a finite element method for evaluating the safety of turbine blade water erosion defects, comprising the following steps: Step 1, determining the water erosion defect area of ​​the blade, either through full three-dimensional aerodynamic flow field analysis or by determining the water erosion area based on the blade's on-site operating conditions. Record the water erosion defect areas determined during each major overhaul of the unit, and identify the severely damaged areas as water erosion defect areas; Step 2, establishing a blade water erosion defect model, based on on-site operating conditions and the results of the full three-dimensional aerodynamic flow field analysis. Combined models are established within the water erosion defect area, taking different depths and lengths. The upper limit of the model's defect depth and length represents the allowable values ​​for blade strength and vibration; Step 3, performing finite element analysis on the blade water erosion defect model to determine the upper limit of the blade water erosion defect size. The finite element analysis includes static stress, dynamic frequency, and dynamic stress analysis; wherein: static stress is based on finite element elastic analysis. The analysis and evaluation process includes three steps: 1) analyzing the average stress and local peak stress at the critical interface of the blade; 2) analyzing the dynamic frequency based on the prestress at the operating speed to determine whether the resonant speed of the blade avoids the critical operating range; 3) analyzing the dynamic stress based on harmonic response analysis, using the pressure calculated from the fluid as the excitation force applied to the blade structure surface for response analysis to determine whether the dynamic stress of the blade meets the vibration resistance limit of the blade material; 4) evaluating the safety of the blade's water erosion defect structure, determining the upper limit of the defect depth and length of the blade model, and obtaining the blade's static stress water erosion defect limit, dynamic frequency water erosion defect limit, and dynamic stress water erosion defect limit based on the finite element analysis results in step 3. The minimum value of the blade's water erosion defect size among the three limits is used to determine whether the target blade exceeds the water erosion defect size limit. If the blade's water erosion defect exceeds this size limit, the blade will be at risk of failure; if the blade's water erosion defect is less than this size limit, the blade can continue to operate.

[0052] Example 2, combined with Figures 1-6 This embodiment describes a finite element method for evaluating the safety of turbine blades against water erosion damage. Specifically:

[0053] Step 1: Determine the water erosion damage area on the blade. The water erosion damage area on the blade is mainly determined through two methods.

[0054] First, a full three-dimensional aerodynamic flow field analysis of the blades is performed to obtain the streamlines of the blades under different operating conditions (e.g., Figure 3 ) and humidity (e.g.) Figure 4 Based on the actual water erosion damage of the blades after the power plant's operation, the water erosion areas of the blades are determined; specifically:

[0055] First, a fluid computational geometric model of the blades is established. The model adopts a cyclic periodic symmetric model, and the geometric parameters include the mean diameter of the stationary and moving blades, blade height, root expansion angle, number of blades, and blade rotation speed.

[0056] Then, fluid meshing is performed based on the geometric model. The mesh adopts a structured hexahedral mesh, and the mesh independence is verified. The number of meshes with the optimal computational efficiency and accuracy is selected.

[0057] Then, boundary parameters were applied to the fluid mesh model. The fluid state was viscous and compressible, and the fluid satisfied the physical conservation laws. Water and water vapor were used as the working fluids. The SST turbulence model was adopted, and the wall was set as a smooth and adiabatic boundary condition. The stationary blade flow domain was set as a stationary domain, and the moving blade flow domain was set as a swirl velocity of 3000 rpm. The total pressure and total enthalpy at the flow domain inlet and the static pressure at the outlet were calculated to obtain the streamlines and humidity of the blade under different operating conditions.

[0058] Finally, based on the water erosion damage of the blades after actual operation of the power plant, the water erosion areas of the blades were determined, and according to... Figure 3 As can be seen from the streamlines of the blade, when the blade is operating at a load of over 41%, water vapor mainly erodes the inlet side of the blade. Since the airflow velocity at the tip of the blade is greater than that at the root, the inlet side of the blade tip is selected as the water erosion defect area. When the blade is operating at a load of less than 41%, water erosion occurs at the outlet side of the blade root due to eddies and backflow in the flow channel. Therefore, the outlet side of the blade root is selected as the water erosion defect area.

[0059] Secondly, the water erosion area is determined based on the on-site operation of the blades, such as... Figure 5 As shown, the water erosion damage areas of the blades were identified during each major overhaul of the unit, and the areas with more severe damage were given special attention.

[0060] Step 2: Establish a water erosion damage model for the blades.

[0061] A blade water erosion damage model was established based on actual operating conditions and the results of full three-dimensional aerodynamic flow field analysis. For example... Figure 6As shown, the water erosion defect models include the following types: First, the blade's main water erosion defect area is only the air intake side at the blade tip. Using the original design model as the baseline, combined models are established with different depths (in increments of 2 mm) and lengths (in increments of 50 mm) on the air intake side. The upper limits of the model's defect depth and length are the allowable values ​​for the blade's strength and vibration. Second, the blade's water erosion defect area is only the air outlet side at the blade root. Using the original design model as the baseline, combined models are established with different depths (in increments of 2 mm) and lengths (in increments of 50 mm) on the air outlet side at the blade root. That is, water erosion defect models of different heights and depths are established within the same water erosion area. For water erosion in the height direction, one model is established every 50 mm; for water erosion in the depth direction, one model is established every 2 mm. The upper limits of the model's defect depth and length are the allowable values ​​for the blade's strength and vibration. Third, when there are defects on both the inlet side at the top of the blade and the outlet side at the root of the blade, the original design model is used as the baseline model, and combined models are established with different depths (with a defect increment of 2 mm) and different lengths (with a defect increment of 50 mm). The upper limit of the defect depth and length of the model is the allowable value of the blade's strength and vibration.

[0062] Step 3: Perform finite element analysis on the blade water erosion defect model to determine the upper limit of the blade water erosion defect size.

[0063] Finite element analysis includes static stress, dynamic frequency, and dynamic stress analysis. Static stress analysis is based on finite element elastic analysis to analyze and assess the average stress and local peak stress at the critical interface of the blade. Dynamic frequency analysis is based on prestress at the operating speed to analyze and assess whether the resonant speed of the blade avoids the critical operating range. Dynamic stress analysis is based on harmonic response analysis, using the pressure calculated from the fluid as the excitation force, applied to the blade structure surface for response analysis, to analyze and assess whether the dynamic stress of the blade meets the vibration resistance limit of the blade material.

[0064] Finite element analysis (FEM) was performed on the blade water erosion defect model. The FEM model adopted a cyclic symmetric configuration, with the cyclic symmetric body consisting of a blade and rotor groove of one pitch. Contact settings were used between blade shrouds, tie rods, blade roots, and between blade roots and rotor grooves. Parameters such as material density, elastic modulus, and Poisson's ratio were set for the blade and rotor. Structured hexahedral meshes were used for both the blade and rotor, with a mesh side length ratio controlled at 3:1, employing first-order reduced integral solid elements. The blade static loads included centrifugal force and steam pressure. Centrifugal force was determined by the rotational angular velocity of the blade and rotor, while steam pressure, based on fluid analysis results, was applied to the blade surface after fluid-structure interaction for static analysis. The blade dynamic frequencies were calculated between 2000 rpm and 3300 rpm, with dynamic frequency analysis performed every 500 rpm, and resonant speeds and frequencies were plotted in Campbell plots. Based on the blade fluid calculation results, the blade excitation force is given through fluid-structure interaction, and the excitation factor of the excitation force is given according to the blade order and nodal diameter. Combined with the blade structure type, the damping coefficient is given, and the dynamic stress analysis of the blade is carried out using the harmonic response method.

[0065] Based on the finite element static strength analysis results of the blade water erosion defect model, the peak stress of the blade is tested for static strength. When the peak stress of the blade water erosion defect model exceeds the allowable value of the blade material, the water erosion defect structure at this point is the upper limit size under the static strength test. The formula for the static stress test of the blade is as follows:

[0066] Peak stress σ F =(σ 2 +3τ 2 ) 1 / 2 (1)

[0067] [σ]= K i / S i (2)

[0068] Peak stress σ F <[σ](3)

[0069] In the formula: σ is the principal stress; τ is the shear stress; K i S represents the yield strength of the material. i σ is the safety factor; F [σ] represents the peak stress of the blade; [σ] represents the allowable static strength of the blade.

[0070] Based on the finite element dynamic frequency analysis results of the blade water erosion defect model, dynamic frequency assessment is performed based on the blade Campbell diagram. When the dynamic frequency of the blade water erosion defect model exceeds the allowable safe range (operating frequency * 6% ~ operating frequency * 3%), the blade water erosion defect structure at this point is the upper limit size under the dynamic frequency assessment. The dynamic frequency assessment formula for the blade is as follows:

[0071] Bending vibration frequency

[0072] Torsional vibration frequency

[0073] Operating frequency * 6% < f 01 or f 02 <Working frequency * 3% (6)

[0074] In the formula: f 01 f is the bending vibration frequency; 02 ρ is the torsional vibration frequency; L is the blade height; A is the cross-sectional area; ρ is the blade material density; E is the material elastic modulus; G is the shear modulus; T0 is the torsional stiffness geometric factor; I0 is the polar moment of inertia of the blade section.

[0075] Based on the finite element dynamic stress analysis results of the blade water erosion defect model, dynamic stress assessment is performed based on the vibration resistance strength curve of the blade material. When the dynamic stress of the blade water erosion defect model exceeds the allowable value of the blade material, the water erosion defect structure at this point is the upper limit size under the dynamic stress assessment. The dynamic stress assessment formula for the blade is as follows:

[0076]

[0077] [σ a ]=σ -1 (8)

[0078]

[0079] In the formula: π is the dynamic stress of the blade; π is pi; ω is the circular frequency of vibration; δ is the attenuation rate; F M For modal forces; M M For modal mass; σ v σ is the modal stress; S is the excitation factor; β is the stress concentration factor; [σ a ] represents the allowable dynamic stress of the material; σ -1 This represents the fatigue limit of the material.

[0080] Step 4: Assess the safety of the water erosion damage structure of the blade and determine the upper limit of the depth and length of the damage in the blade model.

[0081] Based on the finite element analysis results of the blade water erosion defect model, the water erosion defect limit dimensions of the blade under static strength test, dynamic frequency test, and dynamic strength test are obtained. The minimum value among these three test limits is taken as the blade's water erosion defect limit dimension. Thus, the blade's water erosion defect limit can be determined. The determination method is as follows: When the blade water erosion defect reaches the minimum value among the three limit dimensions, the blade is at risk of failure. When the blade water erosion defect is less than the minimum value among the three limit dimensions, the blade can continue to operate.

[0082] Blade water erosion damage limit = min{limit size} 静应力 Limit dimensions 动频率 Limit dimensions 动应力} (10).

[0083] The above embodiment is a finite element method for evaluating the safety of turbine blades against water erosion defects. This method combines numerical analysis with actual operating conditions to quantitatively determine the limit dimensions of water erosion defects in the blades. Blade failure due to defects during operation can lead to the failure of the entire blade ring, and in severe cases, can cause cylinder penetration, resulting in equipment damage and personnel injuries. Using the above embodiment, long-term maintenance strategies for the blades can be developed, reducing operational risks and avoiding downtime accidents caused by blade failures. It is simple to operate, highly versatile, and can be widely applied to turbine blades with water erosion defects.

[0084] The embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above descriptions are merely embodiments of this application and are not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made based on the technical solution of this application should be included within the scope of protection of this application.

Claims

1. A finite element method for evaluating the safety of turbine blades against water erosion damage, characterized in that, Includes the following steps: Step 1: Identify the water erosion damage area on the blade The water erosion area can be determined by conducting a full three-dimensional aerodynamic flow field analysis of the blades, or by determining the water erosion area based on the blades' on-site operating conditions. The water erosion defect area of ​​the blades can be recorded during each major overhaul of the unit, and the severely damaged area can be identified as the water erosion defect area. Step 2: Establish a model of water erosion damage to the blades. Based on the on-site operation and the results of the full three-dimensional aerodynamic flow field analysis, a blade water erosion defect model was established. Different depths and lengths were selected in the blade water erosion defect area to establish a combined model. The upper limit of the defect depth and length of the model is the allowable value of the blade's strength and vibration. Step 3: Perform finite element analysis on the blade water erosion defect model to determine the upper limit of the blade water erosion defect size. Finite element analysis includes static stress, dynamic frequency, and dynamic stress analysis; Among them: static stress is based on finite element elastic analysis to analyze and evaluate the average stress and local peak stress at the dangerous interface of the blade; dynamic frequency is based on the prestress at the operating speed to analyze and evaluate whether the resonant speed of the blade avoids the dangerous operating range. Dynamic stress is based on harmonic response analysis. The pressure calculated by the fluid is used as the excitation force and applied to the surface of the blade structure for response analysis. The analysis and evaluation are conducted to determine whether the dynamic stress of the blade meets the vibration resistance limit of the blade material. Step 4: Assess the safety of the water erosion damage structure on the blade and determine the upper limit dimensions of the damage depth and length of the blade model. Based on the finite element analysis results in step 3, the static stress water erosion defect limit, dynamic frequency water erosion defect limit, and dynamic stress water erosion defect limit of the blade are obtained. The minimum value of the water erosion defect size among the three limits is taken as the criterion for judging whether the target blade exceeds the water erosion defect size limit. If the water erosion defect of the blade exceeds this size limit, the blade will be at risk of failure; if the water erosion defect of the blade is less than this size limit, the blade can continue to operate.

2. The finite element method for evaluating the safety of water erosion damage to turbine blades according to claim 1, characterized in that: In step 1, a full three-dimensional aerodynamic flow field analysis of the blade is performed to obtain the streamlines and humidity of the blade under different operating conditions. Combined with the water erosion damage of the blade after actual operation of the power plant, the water erosion area of ​​the blade is determined. Specifically: First, a fluid calculation geometric model of the blade is established. The model adopts a cyclic periodic symmetric model. The geometric parameters include the mean diameter of the stationary and moving blades, blade height, root expansion angle, number of blades, and blade rotation speed. Then, based on the geometric model, the fluid mesh was generated using a structured hexahedral mesh, and mesh independence was verified. The optimal number of meshes for computational efficiency and accuracy was selected. Next, boundary parameters were applied to the fluid mesh model. The fluid state was viscous and compressible, and the fluid satisfied the physical conservation laws. Water and water vapor were used as the working fluids, and the SST turbulence model was adopted. Smooth and adiabatic boundary conditions were used on the wall. The stationary blade flow domain was set as a stationary domain, and the moving blade flow domain was set to a rotation speed of 3000 rpm. The total pressure and total enthalpy at the inlet of the flow domain were calculated, and the static pressure at the outlet was calculated to obtain the streamlines and humidity of the blades under different operating conditions. Finally, based on the water erosion damage of the blades after the actual operation of the power plant, the water erosion area of ​​the blades was determined. When the blades were operating at a load of over 41%, the water vapor mainly eroded the steam inlet side of the blades. Since the airflow velocity at the tip of the blades was greater than that at the root of the blades, the steam inlet side at the tip of the blades was selected as the water erosion damage area. When the blade is operating under a load of less than 41%, water erosion occurs on the steam outlet side of the blade root due to eddies and backflow in the flow channel. The steam outlet side of the blade root is selected as the water erosion defect area.

3. The finite element method for evaluating the safety of water erosion damage to turbine blades according to claim 2, characterized in that: In step 2, water erosion defect models of different heights and depths are established in the same water erosion area. For water erosion defects in the height direction, a model is established every 50 mm; for water erosion defects in the depth direction, a model is established every 2 mm.

4. The finite element method for evaluating the safety of water erosion damage to turbine blades according to claim 3, characterized in that: In step 3, a finite element analysis is performed on the blade water erosion defect model. The finite element calculation model adopts a cyclic symmetric setting. The cyclic symmetric body includes a blade with one pitch and a rotor groove. Contact settings are adopted between the shrouds of the blade, between the tie rods, between the blade roots, and between the blade roots and the groove. The density, elastic modulus, and Poisson's ratio of the materials are set for the blade and the rotor. The blade and rotor mesh adopts a structured hexahedral mesh with the mesh side length ratio controlled at 3:1, and first-order reduced integral solid elements are used. The blade static load includes centrifugal force and steam pressure. The centrifugal force is set by the rotational angular velocity of the blade and rotor. The steam pressure is based on the fluid analysis results and is applied to the blade surface after fluid-structure interaction for static stress analysis. The blade dynamic frequency is calculated between 2000 rpm and 3300 rpm, and dynamic frequency analysis is performed every 100 rpm. The resonant speed and resonant frequency are plotted in the Campbell diagram. Based on the blade fluid calculation results, the blade excitation force is given through fluid-structure interaction, and the excitation factor of the excitation force is given according to the blade order and nodal diameter. Combined with the blade structure type, the damping coefficient is given, and the dynamic stress analysis of the blade is carried out using the harmonic response method.

5. The finite element method for evaluating the safety of water erosion damage to turbine blades according to claim 4, characterized in that: In static stress analysis, when the peak stress of the blade water erosion defect model exceeds the allowable value of the blade material, the water erosion defect structure at this point is the upper limit size under static strength testing. The static stress testing formula for the blade is as follows: Peak stress ; ； Peak stress ; In the formula: Principal stress; Shear stress; The yield strength of the material; For safety factor; This represents the peak stress of the blade. This represents the allowable static strength value for the blade.

6. The finite element method for evaluating the safety of water erosion damage to turbine blades according to claim 5, characterized in that: In dynamic frequency analysis, when the dynamic frequency of the blade water erosion defect model exceeds the allowable safe range, the blade water erosion defect structure at this point is the upper limit size under the dynamic frequency assessment. The dynamic frequency assessment formula for the blade is as follows: Bending vibration frequency ; Torsional vibration frequency ; Operating frequency ; In the formula: The frequency of bending vibration; The frequency of torsional vibration; For the leaf height; The cross-sectional area; Density of the blade material; The elastic modulus of the material; Shear modulus; This is the torsional stiffness geometric factor; Let be the polar moment of inertia of the blade cross section.

7. The finite element method for evaluating the safety of water erosion damage to turbine blades according to claim 6, characterized in that: In dynamic stress analysis, when the dynamic stress of the blade water erosion defect model exceeds the allowable value of the blade material, the blade water erosion defect structure at this point is the upper limit size under the dynamic stress test. The dynamic stress test formula for the blade is as follows: ； ； ； In the formula: For the dynamic stress of the blade; Pi; It is the angular frequency of vibration; The attenuation rate; Modal force; Modal mass; Modal stress; The excitation factor; The stress concentration factor; This refers to the allowable dynamic stress value of the material. This represents the fatigue limit of the material.

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