A turbine wide load blade aerodynamic-structure coupling simulation design method

Abstract

The present application relates to the technical field of blade simulation design, in particular to a steam turbine wide load blade aerodynamic-structure coupling simulation design method, comprising: based on the initial geometric configuration of the blade, a three-dimensional unsteady steam compressible flow model of the blade channel is established in the fluid solver to simulate the strong unsteady steam excitation in the wide load range; a blade-disk finite element model is built in the structural dynamics solver, and the blade root contact nonlinearity and material nonlinearity conditions are included; a two-way real-time data exchange interface of the two types of solvers is constructed, the time-varying aerodynamic load of the blade wet surface is extracted and mapped as the structural model node force boundary condition; the blade transient dynamic response and dynamic displacement field are solved, and through coupling iterative operation, the blade aerodynamic-structure integrated coupling simulation calculation under wide load working condition is completed, and the interaction relationship between the variable working condition airflow excitation and the structural dynamic deformation is truly reflected.

Description

Technical Field

[0001] This invention relates to the field of blade simulation design technology, and in particular to a method for aerodynamic-structural coupling simulation design of turbine blades under wide loads. Background Technology

[0002] As the operating conditions of steam turbine units continue to expand, the steam flow state around the blades exhibits significant unsteady characteristics under wide-load variable operating conditions, and complex airflow excitation continuously acts on the blade surface. Conventional aerodynamic simulations mostly use steady flow calculation models, which are only suitable for solving the flow field under a single steady condition. They cannot cover the changes in flow characteristics caused by parameter variations over a wide load range, and it is difficult to reproduce the unsteady airflow disturbances generated during variable load processes. The airflow load calculations cannot accurately reflect the dynamic changes in the actual operating process.

[0003] Traditional blade structure simulation modeling often involves idealization and simplification, weakening the contact relationship at the blade root assembly location, ignoring the nonlinear variation characteristics of the material itself, and resulting in a linearized assumption in the construction of the structural model. The aerodynamic calculation module and the structural dynamics calculation module operate independently, lacking a real-time communication channel between the modules. Aerodynamic loads are mostly imported using a unidirectional static method, making it impossible to synchronously transfer dynamic loads.

[0004] Single, isolated simulation methods cannot capture the interaction between airflow and blade structural deformation, making closed-loop iterative calculations difficult. The refined design of modern turbine blades under wide-load conditions demands higher standards for aerodynamic load capture accuracy, structural nonlinear characterization capabilities, and multi-physics collaborative calculation capabilities. The limitations of existing simulation methods are becoming increasingly apparent, failing to meet the design requirements of multi-physics collaborative simulation of blades under wide-load scenarios. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and propose an aerodynamic-structural coupling simulation design method for steam turbine blades under wide loads.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a steam turbine wide-load blade aerodynamic-structural coupling simulation design method, comprising: Based on the initial geometric configuration of the turbine blades, a three-dimensional unsteady steam compressible flow model of the blade passage is established in the computational fluid dynamics solver. The three-dimensional unsteady steam compressible flow model is used to simulate strong unsteady steam excitation under a wide load range. A finite element structural dynamics model of the blade and the disk is established in the structural dynamics solver. The finite element structural dynamics model takes into account the contact nonlinearity and material nonlinearity at the blade root connection. Construct a bidirectional real-time data exchange interface connecting the computational fluid dynamics solver and the structural dynamics solver; Under the action of the bidirectional real-time data exchange interface, the time-varying aerodynamic loads acting on the wet surface are extracted from the three-dimensional unsteady steam compressible flow model, and the time-varying aerodynamic loads are mapped to the nodal force boundary conditions on the finite element structural dynamics model. The finite element structural dynamic model is driven to solve the transient dynamic response of the blade under the nodal force boundary conditions, thereby obtaining the dynamic displacement field of the blade; The dynamic displacement field of the blade is calculated using a coupled iterative method to obtain the coupled simulation results of the blade.

[0007] As a further aspect of the present invention, the step of establishing a three-dimensional unsteady steam compressible flow model of the blade passage in the computational fluid dynamics solver includes: Based on the geometric shape of the turbine blades and adjacent stator blades, the fluid computation domain of the blade passage is extracted. The fluid computation domain includes the main channel, the blade tip clearance region, and the near-wall boundary layer region. The fluid computational domain is divided into unstructured hybrid meshes, and the boundary layer mesh is refined in key areas of the blade surface and endwall to generate a computational mesh system suitable for solving unsteady flows. The physical properties of the steam working fluid are defined by adopting the equation of state and transport coefficient model applicable to the actual physical properties of steam. Set the inlet total pressure, total temperature boundary conditions and outlet static pressure boundary conditions corresponding to the wide load operating range, and specify the treatment method for the dynamic and static blade interface. A large eddy simulation turbulence model based on scale-adaptive simulation was selected, and combined with dynamic mesh technology, to establish a three-dimensional unsteady steam compressible flow model capable of simulating the entire process from startup, variable load to deep peak shaving.

[0008] As a further aspect of the present invention, the step of establishing a finite element structural dynamics model of the blade and the disk in the structural dynamics solver includes: Based on the solid geometric model of the blade, high-order hexahedral elements are used to mesh the blade solid, and local mesh refinement is performed in the transition area between the blade body and the tenon and in the stress concentration area of ​​the pull hole. The wheel disk is simplified in modeling, while the rim part connected to the blade tenon is retained. The mesh is generated using a mixture of tetrahedral and hexahedral elements. In the finite element preprocessing, the nonlinear constitutive relations of the blade and disk materials are defined. The nonlinear constitutive relations include the elastic modulus, yield strength and cyclic plastic hardening parameters that vary with temperature. Set up the contact pair between the leaf root tenon and the wheel disk tenon, and define the friction coefficient and contact algorithm parameters to simulate the contact nonlinearity; Apply a rotational speed constraint to the center of the wheel and constrain the radial and axial displacements of the inner surface of the wheel. After assigning material properties, setting constraints and loads, the finite element structural dynamic model is formed, which prepares for solving transient dynamic response.

[0009] As a further aspect of the present invention, a bidirectional real-time data exchange interface is constructed connecting the computational fluid dynamics solver and the structural dynamics solver, including: Set the time step for the coupling analysis and divide the total time of the coupling analysis into multiple coupling time substeps; At the beginning of each coupled time substep, the bidirectional real-time data exchange interface receives the pressure distribution and shear stress distribution of the wetted surface of the blade under the current steam flow field from the computational fluid dynamics solver. The pressure distribution and shear stress distribution together constitute the time-varying aerodynamic load. The loosely coupled partitioning algorithm is invoked to conservely interpolate the time-varying aerodynamic load from the fluid mesh nodes of the computational fluid dynamics solver to the structural finite element mesh nodes of the structural dynamics solver, thereby generating the nodal force boundary conditions. After the structural dynamics solver completes the transient dynamic response solution within the current coupled time substep, the bidirectional real-time data exchange interface receives the dynamic displacement field characterizing the blade deformation and motion from the structural dynamics solver. The loosely coupled partitioning algorithm is invoked again to transfer the dynamic displacement field from the structural finite element mesh node of the structural dynamics solver to the fluid mesh node of the computational fluid dynamics solver, driving the fluid computational mesh to perform corresponding deformation and motion. After completing the bidirectional transfer of the time-varying aerodynamic load and the dynamic displacement field, the bidirectional real-time data exchange interface sends a synchronization signal to the computational fluid dynamics solver and the structural dynamics solver, enabling the computational fluid dynamics solver and the structural dynamics solver to enter the next coupled time substep of calculation.

[0010] As a further aspect of the present invention, the working principle of the loosely coupled partitioning algorithm is as follows: During the initialization phase, a spatial positional mapping between the two sets of mesh nodes is established based on the fluid mesh of the computational fluid dynamics solver and the structural finite element mesh of the structural dynamics solver. Calculate the overlap area weighting coefficient between the fluid mesh surface element and the structural finite element surface element, and combine the overlap area weighting coefficient with the element shape function to construct the load transfer matrix from the fluid mesh node to the structural mesh node; By utilizing the principle of conservation interpolation, the aerodynamic load vector on the fluid grid node is multiplied by the load transfer matrix to obtain the equivalent nodal force acting on the structural grid node, ensuring the global conservation of force and torque during the transfer process. In the displacement transfer process from the structural mesh to the fluid mesh, a displacement transfer matrix is ​​constructed based on the radial basis function interpolation method. The radial basis function interpolation method uses the displacement of the structural mesh nodes as known quantities and obtains the displacement of the fluid mesh boundary nodes by solving the linear system. Within each coupling time substep, the load transfer matrix and the displacement transfer matrix are queried to achieve fast interpolation and exchange of data. At the end of each coupling time step, the energy conservation error of the transferred data is monitored and corrected to ensure the numerical stability of the bidirectional coupling solution.

[0011] As a further aspect of the present invention, driving the finite element structural dynamics model to solve the transient dynamic response of the blade under the nodal force boundary conditions includes: In the structural dynamics solver, initial conditions are set for the finite element structural dynamics model, including that the initial displacement field and initial velocity field of the blade are both zero. In the transient solver, an implicit time integration algorithm is selected, and a calculation time step consistent with the time step of the coupled analysis is set. Within each coupling time substep, the nodal force boundary conditions transmitted from the bidirectional real-time data exchange interface are applied to the corresponding nodes on the blade surface. Considering the material nonlinearity and the contact nonlinearity, the nonlinear dynamic equilibrium equation is solved iteratively within the calculation time step to obtain the displacement, velocity and acceleration of each node of the blade at the end of the current coupling time substep; The results of each time step are accumulated to obtain the time history response of the blade during the entire coupled simulation time. The time history response is the dynamic displacement field.

[0012] As a further aspect of the present invention, the dynamic displacement field of the blade is subjected to coupled iterative calculation to obtain the coupled simulation results of the blade, including: Through the bidirectional real-time data exchange interface, the dynamic displacement field of the blade is fed back as the dynamic boundary condition of the three-dimensional unsteady steam compressible flow model, thereby updating the shape and position of the computational grid in the steam flow region and completing a bidirectional fluid-structure interaction iterative calculation. Repeat the steps from extracting time-varying aerodynamic loads to completing one bidirectional fluid-structure interaction iterative calculation until the dynamic displacement field and steam flow field of the blade both reach the preset convergence criteria, and obtain the coupled simulation results under the convergence state. Based on the coupled simulation results under the convergence state, the aerodynamic damping characteristics, dynamic stress distribution, and flutter stability boundary of the blade are analyzed in the target wide load range.

[0013] As a further aspect of the present invention, the dynamic displacement field of the blades is fed back as the dynamic boundary conditions of the three-dimensional unsteady steam compressible flow model through the bidirectional real-time data exchange interface, thereby updating the shape and position of the computational grid in the steam flow region, including: The bidirectional real-time data exchange interface transmits the dynamic displacement field of the blade to the dynamic mesh module of the computational fluid dynamics solver. The dynamic mesh module updates the position of the mesh nodes in the fluid computational domain by using a combination of spring approximation smoothing and local mesh re-subdivision based on the transmitted displacement data. In the region near the blade surface, the mesh deformation strictly follows the displacement amount given by the dynamic displacement field, ensuring the consistency of the fluid-solid interface geometry; In the fluid region far from the blade wall, the boundary displacement is smoothly transferred to the internal mesh nodes by the spring approximation smoothing method to prevent mesh distortion; When the quality of a local mesh cell falls below a preset threshold due to deformation, the local mesh is re-divided, and a new high-quality mesh is automatically generated in the local area with excessive deformation. After the mesh update is completed, the three-dimensional unsteady steam compressible flow model performs steam flow field calculations in the next coupled time substep based on the new mesh shape and position.

[0014] As a further aspect of the present invention, the step of repeatedly executing the process from extracting the time-varying aerodynamic load to completing one bidirectional fluid-structure interaction iterative calculation until both the dynamic displacement field and the steam flow field of the blade reach the preset convergence criterion includes: Within each coupled time substep, after completing one bidirectional data exchange and each solution, the incremental norm of the key physical quantities of the dynamic displacement field and the steam flow field is calculated. Define flow field convergence criteria and structural field convergence criteria. The flow field convergence criteria is that the absolute value of the average pressure fluctuation rate on the blade surface is less than a first threshold, and the structural field convergence criteria is that the rate of change of the maximum dynamic strain energy of the blade is less than a second threshold. During the iteration of each coupling time substep, the average pressure fluctuation rate on the blade surface and the rate of change of the maximum dynamic strain energy of the blade are monitored simultaneously. When the average pressure fluctuation rate on the blade surface and the rate of change of the maximum dynamic strain energy of the blade simultaneously satisfy the flow field convergence criterion and the structural field convergence criterion, the coupling calculation within the coupling time substep is determined to have converged. If the convergence criterion is not met, the steps from extracting the time-varying aerodynamic load to completing one bidirectional fluid-structure interaction iterative calculation will continue to be executed within the same coupling time substep, and the substep iteration will be performed until the convergence criterion is met or the maximum number of substep iterations is reached. Once the calculation of the coupled time substep has converged, the calculation process proceeds to the next coupled time substep, repeating the steps from extracting the time-varying aerodynamic load to completing one bidirectional fluid-structure interaction iterative calculation, until all coupled time substeps have been calculated.

[0015] As a further aspect of the present invention, based on the coupled simulation results under the convergent state, the aerodynamic damping characteristics, dynamic stress distribution, and flutter stability boundary of the blade within the target wide load range are analyzed, including: From the coupled simulation results under the convergence state, extract the time-domain response data of the blades under multiple typical load steady-state operating conditions; Fourier transform is performed on the time-domain response data at each operating point to identify the dominant frequency and mode shape of blade vibration; At the dominant frequency, the aerodynamic damping characteristics are quantified by calculating the sign and magnitude of the work done by the aerodynamic force on the blade within one vibration cycle. From the solution results of the finite element structural dynamic model, the equivalent stress time history of each blade element during the entire coupled simulation time is extracted, and the dynamic stress distribution is statistically obtained, including the maximum dynamic stress value and its location. By systematically changing the inlet flow rate or back pressure parameters to simulate different loads, and repeatedly coupling the simulation process, the critical operating point of the blade vibration response from steady to divergent is recorded. By summarizing vibration stability data under different loads, a curve of blade amplitude changing with load is plotted, and the load point where the amplitude begins to increase sharply is identified as the flutter stability boundary.

[0016] Compared with the prior art, the advantages and positive effects of the present invention are as follows: Based on a three-dimensional unsteady steam compressible flow model, the flow field model of the blade passage is completed, which can characterize the airflow operation state under varying load conditions and fully present the strong unsteady steam excitation formed during variable load processes. Adhering to the inherent properties of compressible steam flow, it fully captures the temporal changes of aerodynamic loads on the blade surface, avoids the oversimplification of flow field dynamics in steady simulation models, and fully restores the airflow interaction patterns under complex operating environments. This ensures that the calculated aerodynamic load state closely matches the fluid variation patterns in actual operation, thus improving the comprehensive characterization capability of fluid simulation under wide load and variable operating conditions.

[0017] The structural dynamics modeling process incorporates nonlinear contact behavior at the blade root position and combines it with nonlinear material properties to complete the model construction, mitigating model distortion caused by linear simplification assumptions. A bidirectional real-time data exchange interface is established between the fluid solver and the structural dynamics solver to achieve cross-module transfer of time-varying aerodynamic loads and transformation of nodal force boundary conditions. The transient dynamic response of the blade is solved using real-time airflow loads as input conditions to obtain the global dynamic displacement field and continuously conduct multi-round coupled iterative calculations. The data interaction barriers between fluid calculations and structural calculations are broken down, changing the calculation form of unidirectional load import to realize the mutual influence feedback between fluid action and structural deformation, enriching the calculation dimensions of transient dynamic response, strengthening the linkage of multi-physics synchronous calculations, continuously improving the overall computational logic of coupled simulation, and adapting to the simulation requirements of multi-field coupling of blades under wide load continuous variable conditions. Attached Figure Description

[0018] Figure 1 This is a state diagram of the aerodynamic-structural coupling simulation design method for wide-load turbine blades described in this invention. Figure 2 Flowchart for establishing a three-dimensional unsteady steam compressible flow model in a blade passage; Figure 3 This is a flowchart illustrating the working principle of the loosely coupled partitioning algorithm. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0020] In the description of this invention, it should be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, in the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0021] See Figure 1 The present invention provides an aerodynamic-structural coupling simulation design method for turbine blades under wide loads, the overall implementation scheme of which is as follows: Based on the initial geometry of the turbine blades, a three-dimensional unsteady steam compressible flow model of the blade passage is established in the computational fluid dynamics (CFD) solver. This model is used to simulate strong unsteady steam excitation under a wide load range. A finite element structural dynamics model of the blade and turbine disk is established in the structural dynamics solver, considering contact nonlinearity and material nonlinearity at the blade root connection. A bidirectional real-time data exchange interface is constructed connecting the CFD solver and the structural dynamics solver. Under the action of this interface, time-varying aerodynamic loads acting on the wetted surface are extracted from the three-dimensional unsteady steam compressible flow model and mapped to nodal force boundary conditions on the finite element structural dynamics model. The finite element structural dynamics model is then driven to solve for the transient dynamic response of the blade under these nodal force boundary conditions, obtaining the dynamic displacement field of the blade. Coupled iterative calculations are performed on the dynamic displacement field to obtain the coupled simulation results.

[0022] In one embodiment of the present invention, see [reference] Figure 2 Based on the geometry of the turbine blades and adjacent stator blades, the fluid computational domain of the blade passage is extracted. This domain includes the main flow passage, the tip clearance region, and the near-wall boundary layer region. An unstructured hybrid mesh is generated for this computational domain, with boundary layer mesh refinement applied to critical regions on the blade surface and endwall, producing a computational mesh system suitable for solving unsteady flows. A state equation and transport coefficient model applicable to the actual physical properties of steam are used to define the physical properties of the steam working fluid. Inlet total pressure, total temperature, and outlet static pressure boundary conditions are set for a wide load range, and the dynamic-stator blade interface treatment method is specified. A large eddy simulation turbulence model based on scale-adaptive simulation is selected, combined with dynamic mesh technology, to establish a three-dimensional unsteady compressible steam flow model capable of simulating the entire process from startup, load variation to deep peak shaving.

[0023] Based on the solid geometric model of the blade, high-order hexahedral elements were used to mesh the blade solid, with local mesh refinement in the transition zone between the blade body and the tenon, and in areas of stress concentration at the lamination holes. The wheel disk was simplified, retaining only the rim portion connected to the blade tenon, and meshed using a hybrid tetrahedral and hexahedral element model. In the finite element preprocessing, nonlinear constitutive relations for the blade and wheel disk materials were defined, including temperature-dependent elastic modulus, yield strength, and cyclic plastic hardening parameters. A contact pair between the blade root tenon and the wheel disk tenon was established, defining the friction coefficient and contact algorithm parameters to simulate the contact nonlinearity. A rotational speed constraint was applied to the center of the wheel disk, and radial and axial displacements of the inner surface of the wheel disk were also constrained. After assigning material properties, setting constraints and loads, the finite element structural dynamic model was formed.

[0024] In the specific implementation, based on the geometry of the last-stage moving blade and guide vane of a certain type of 600 MW supercritical steam turbine, the fluid computational domain of the blade passage was extracted. The fluid computational domain includes the main flow passage from the guide vane outlet to the downstream of the moving blade, a 1.5 mm high blade tip clearance region, and a near-wall boundary layer region. An unstructured hybrid mesh was generated for the fluid computational domain. Boundary layer mesh refinement was applied to key areas on the surfaces of the moving and stationary blades, and on the casing and hub endwalls. The height of the first layer mesh was set to 2e-6 meters to ensure that the y+ value is less than 1, generating a computational mesh system containing approximately 12 million polyhedral core elements and five layers of prism boundary layer elements. During the mesh generation process, the following formula was used to evaluate the quality of the mesh elements:

[0025] in: Indicates the quality coefficient of the mesh element. Represents the volume of a mesh cell. Indicates the grid cell number The area of ​​each face. Indicates the number of faces in a mesh cell. It is a normalization constant related to the element type. This formula is used to monitor and control the quality of the generated mesh. In areas with high curvature, such as the leading and trailing edges of blades, local mesh refinement can be achieved... The value exceeds the set threshold. The IAPWS-IF97 equation of state, applicable to the actual physical properties of steam, and the Sutherland transport coefficient model based on kinetic theory are used to define the physical properties of the steam working fluid. Inlet total pressure, total temperature, and outlet static pressure boundary conditions are set for a wide load range covering 30% to 100% of rated load, and the dynamic-stator interface treatment is specified as a transient rotor-stator interface. A large eddy simulation turbulence model based on scale-adaptive simulation, combined with dynamic mesh technology, is selected to establish a three-dimensional unsteady steam compressible flow model capable of simulating the entire process from startup, load variation to deep peak shaving.

[0026] In some embodiments, based on the solid geometric model of the blade and the disk, the blade solid is meshed using 20-node hexahedral elements. Local mesh refinement is performed in the transition area between the blade body and the fir tree tenon, and at the stress concentration areas of the two lamination holes, with a minimum element size of 0.5 mm. The disk is simplified in modeling, retaining the rim portion connected to the blade tenon, and meshed using a hybrid of 10-node tetrahedral and 20-node hexahedral elements. In the finite element preprocessing, the nonlinear constitutive relations of the blade and disk materials are defined. The nonlinear constitutive relations include the elastic modulus, yield strength, and cyclic plastic hardening parameters that vary with temperature. The yield strength data of the blade material at 500 degrees Celsius is taken from a material handbook. A face-to-face contact pair is set between the fir tree tenon tooth surface at the blade root and the tenon tooth surface of the disk. The friction coefficient is defined as 0.15, and the contact algorithm parameters are defined as the augmented Lagrangian method to simulate contact nonlinearity. A rotational speed constraint of 3000 rpm is applied at the center of the disk, and the radial and axial displacements of the inner surface of the disk are constrained. After assigning material properties, setting constraints and loads, a finite element structural dynamics model is formed. It can be understood that higher-order hexahedral elements have higher numerical accuracy than tetrahedral elements when calculating the structural dynamic response, while local mesh refinement can more accurately capture stress gradient changes.

[0027] In one embodiment of the present invention, the process of constructing a bidirectional real-time data exchange interface connecting the computational fluid dynamics solver and the structural dynamics solver includes: setting the time step of the coupled analysis and dividing the total time of the coupled analysis into multiple coupled time substeps. At the beginning of each coupled time substep, the bidirectional real-time data exchange interface receives the pressure distribution and shear stress distribution of the wetted surface of the blade under the current steam flow field from the computational fluid dynamics solver. The pressure distribution and shear stress distribution together constitute the time-varying aerodynamic load. A loosely coupled partitioning algorithm is invoked to conservely interpolate the time-varying aerodynamic load from the fluid mesh nodes of the computational fluid dynamics solver to the structural finite element mesh nodes of the structural dynamics solver, generating the nodal force boundary conditions. After the structural dynamics solver completes the transient dynamic response solution within the current coupled time substep, the bidirectional real-time data exchange interface receives the dynamic displacement field characterizing the blade deformation and motion from the structural dynamics solver. The loosely coupled partitioning algorithm is invoked again to transfer the dynamic displacement field from the structural finite element mesh nodes of the structural dynamics solver to the fluid mesh nodes of the computational fluid dynamics solver, driving the fluid computational mesh to undergo corresponding deformation and motion. After completing the bidirectional transfer of the time-varying aerodynamic load and the dynamic displacement field, the bidirectional real-time data exchange interface sends a synchronization signal to both the computational fluid dynamics solver and the structural dynamics solver, enabling them to enter the next coupled time substep of calculation.

[0028] The working principle of the loosely coupled partitioning algorithm is as follows: (See below) Figure 3 During the initialization phase, a spatial positional mapping between the nodes of the two meshes is established based on the fluid mesh of the computational fluid dynamics solver and the structural finite element mesh of the structural dynamics solver. The overlap area weighting coefficient between the surface elements of the fluid mesh and the surface elements of the structural finite element mesh is calculated, and this coefficient is combined with the element shape function to construct a load transfer matrix from the fluid mesh nodes to the structural mesh nodes. Using the principle of conservation interpolation, the aerodynamic load vectors on the fluid mesh nodes are multiplied by the load transfer matrix to obtain the equivalent nodal forces acting on the structural mesh nodes, ensuring global conservation of force and torque during the transfer process. During the displacement transfer from the structural mesh to the fluid mesh, a displacement transfer matrix is ​​constructed based on the radial basis function interpolation method. This method uses the displacements of the structural mesh nodes as known quantities and obtains the displacements of the fluid mesh boundary nodes by solving a linear system. Within each coupling time step, rapid interpolation and exchange of data is achieved by querying the load transfer matrix and the displacement transfer matrix. At the end of each coupling time step, the energy conservation error of the transferred data is monitored and corrected.

[0029] In practice, the process of constructing a bidirectional real-time data exchange interface connecting the computational fluid dynamics (CFD) solver and the structural dynamics solver involves setting the time step of the coupled analysis to 2.0e-6 seconds, dividing the total simulation time of a complete variable load process (0.1 seconds) into 50,000 coupled time substeps. At the beginning of each coupled time substep, the bidirectional real-time data exchange interface receives the pressure and shear stress distributions from the CFD solver on approximately 150,000 mesh nodes on the wetted surface of the blade under the current steam flow field. These pressure and shear stress distributions together constitute the time-varying aerodynamic load. A loosely coupled partitioning algorithm is invoked to conservely interpolate the time-varying aerodynamic loads from the fluid mesh nodes of the CFD solver to approximately 80,000 structural finite element mesh nodes of the structural dynamics solver, generating nodal force boundary conditions. After the structural dynamics solver completes the transient dynamic response solution within the current coupled time substep, the bidirectional real-time data exchange interface receives the dynamic displacement field characterizing the blade deformation and motion from the structural dynamics solver. The loosely coupled partitioning algorithm is invoked again to transfer the dynamic displacement field from the structural finite element mesh nodes of the structural dynamics solver to the fluid mesh nodes of the computational fluid dynamics solver, driving the fluid computational mesh to undergo corresponding deformation and motion. After completing the bidirectional transfer of time-varying aerodynamic loads and dynamic displacement fields, the bidirectional real-time data exchange interface sends a synchronization signal to both the computational fluid dynamics solver and the structural dynamics solver, enabling them to enter the next coupled time substep of calculation.

[0030] In some embodiments, the loosely coupled partitioning algorithm works as follows: During the initialization phase, a spatial positional mapping between the nodes of the two meshes is established based on the fluid mesh from the computational fluid dynamics solver and the structural finite element mesh from the structural dynamics solver. The overlapping area weighting coefficient is used between the triangular elements on the surface of the computational fluid dynamics mesh and the quadrilateral elements on the surface of the structural finite element mesh. The specific calculation formula is as follows:

[0031] in: Indicates from the first The fluid mesh node to the first The area weighting coefficient of each structural grid node. Indicates the first The surface unit region associated with each fluid mesh node Indicates the first The surface cell region where each structured mesh node is located. It is the fluid mesh element at the position Shape function at the location, It is an area infinitesimal element. The overlapping area weighting coefficient is combined with the element shape function to construct the load transfer matrix from the fluid mesh nodes to the structural mesh nodes. Using the principle of conservation interpolation, the aerodynamic load vectors on the fluid mesh nodes are multiplied by the load transfer matrix to obtain the equivalent nodal forces acting on the structural mesh nodes, ensuring the global conservation of force and moment during the transfer process. In the displacement transfer process from the structural mesh to the fluid mesh, the displacement transfer matrix is ​​constructed based on the radial basis function interpolation method. This method uses the displacements of the structural mesh nodes as known quantities and obtains the displacements of the fluid mesh boundary nodes by solving a linear system. The selected radial basis function is the thin plate spline function. Within each coupling time substep, rapid interpolation and exchange of data are achieved by querying the load transfer matrix and displacement transfer matrix. At the end of each coupling time step, the energy conservation error of the transferred data is monitored and corrected. It can be understood that the load transfer method based on overlapping area weights ensures that the total aerodynamic force and total torque acting on the wetted surface of the blade are strictly conserved before and after mapping. Thin-plate spline radial basis functions can effectively handle the smooth interpolation problem from structural finite element mesh nodal displacements to fluid mesh nodal displacements.

[0032] In one embodiment of the present invention, driving the finite element structural dynamics model to solve the transient dynamic response of the blade under the nodal force boundary conditions includes: setting initial conditions for the finite element structural dynamics model in the structural dynamics solver, wherein the initial displacement field and initial velocity field of the blade are both zero. In the transient solver, an implicit time integration algorithm is selected, and a calculation time step consistent with the time step of the coupled analysis is set. Within each coupled time substep, the nodal force boundary conditions transmitted from the bidirectional real-time data exchange interface are applied to the corresponding nodes on the blade surface. Considering the material nonlinearity and the contact nonlinearity, the nonlinear dynamic equilibrium equation is iteratively solved within the calculation time step to obtain the displacement, velocity, and acceleration of each node of the blade at the end of the current coupled time substep. The results of each time step are accumulated to obtain the time history response of the blade during the entire coupled simulation time, wherein the time history response is the dynamic displacement field.

[0033] In practical implementation, the process of solving the transient dynamic response of the blade under nodal force boundary conditions using the finite element structural dynamics model includes setting initial conditions for the finite element structural dynamics model in the structural dynamics solver. These initial conditions include zero initial displacement and velocity fields for the blade. In the transient solver, the Newmark-β method of implicit time integration algorithms is selected, and the computation time step is set to 2.0e-6 seconds, consistent with the coupling analysis time step. Within each coupling time substep, the nodal force boundary conditions transmitted from the bidirectional real-time data exchange interface are applied to the corresponding nodes on the blade surface. The nodal force data includes components with three translational degrees of freedom. Considering material nonlinearity and contact nonlinearity, the nonlinear dynamic equilibrium equations are iteratively solved within the computation time step. The incremental iterative form of the nonlinear dynamic equilibrium equations can be expressed as:

[0034] in: The mass matrix represents the structure. Indicates the first A vector of acceleration increments at each time step. Indicates the current speed and stress state The relevant damping matrix, A vector representing the velocity increment. Indicates based on the current displacement and stress state The tangential stiffness matrix, A vector representing the displacement increment. Represents the force vector at the external nodes. This represents the internal resistance vector. By iteratively solving the above equations until the residual norm is less than the set tolerance, the displacement, velocity, and acceleration of each node of the blade at the end of the current coupled time substep are obtained. The results of each time step are accumulated to obtain the time history response of the blade throughout the entire coupled simulation time; the time history response is the dynamic displacement field.

[0035] In some embodiments, solving the nonlinear dynamic equilibrium equations involves updating the material's elastoplastic constitutive relations and determining the contact state. The number of Newton-Raphson iterations within each computation time step is typically between 3 and 7 to balance computational efficiency and accuracy. Optionally, the parameters in the Newmark-β method are set to γ=0.5 and β=0.25 to meet the unconditional stability requirement. Within a specific coupled time substep, the nodal forces applied to specific nodes on the blade surface, the calculated displacements, velocities, and acceleration responses are shown in Table 1. Table 1: Nodal force and response data within a typical coupled time substep

[0036] It is understandable that the implicit time integration algorithm can handle numerical stiffness problems caused by material nonlinearity and contact nonlinearity, allowing for a computational time step consistent with the flow field coupling time step. The accumulated displacement response at each time step constitutes the dynamic displacement field used for feedback to the fluid solver.

[0037] In one embodiment of the present invention, the process of updating the computational grid shape and position of the steam flow region by feeding back the dynamic displacement field of the blade as dynamic boundary conditions through the bidirectional real-time data exchange interface includes: the bidirectional real-time data exchange interface transmits the dynamic displacement field of the blade to the dynamic mesh module of the computational fluid dynamics solver. The dynamic mesh module, based on the transmitted displacement data, uses a combination of spring approximation smoothing and local mesh re-division to drive the position update of the mesh nodes within the fluid computational domain. In the region near the blade surface, mesh deformation strictly follows the displacement amount given by the dynamic displacement field. In the fluid region far from the blade wall, the boundary displacement is smoothly transmitted to the internal mesh nodes using the spring approximation smoothing method. When the mass of a local mesh element falls below a preset threshold due to deformation, local mesh re-division is triggered, automatically generating a new high-quality mesh in the excessively deformed local region. After the mesh update is completed, the three-dimensional unsteady steam compressible flow model performs the steam flow field solution calculation in the next coupled time substep based on the new mesh shape and position.

[0038] The process of extracting time-varying aerodynamic loads and completing one bidirectional fluid-structure interaction (FSI) iterative calculation is repeated until both the dynamic displacement field and the steam flow field of the blade reach the preset convergence criteria. This includes: within each coupling time substep, after completing one bidirectional data exchange and each solution, calculating the increment norm of key physical quantities in the dynamic displacement field and the steam flow field. A flow field convergence criterion and a structural field convergence criterion are defined. The flow field convergence criterion is that the absolute value of the average pressure fluctuation rate on the blade surface is less than a first threshold, and the structural field convergence criterion is that the rate of change of the maximum dynamic strain energy of the blade is less than a second threshold. During the iteration of each coupling time substep, the average pressure fluctuation rate on the blade surface and the rate of change of the maximum dynamic strain energy of the blade are simultaneously monitored. When both the average pressure fluctuation rate on the blade surface and the rate of change of the maximum dynamic strain energy of the blade simultaneously satisfy the flow field convergence criterion and the structural field convergence criterion, the coupling calculation within the coupling time substep is considered to have converged. If the convergence criterion is not met, the process continues within the same coupled time substep, executing the steps from extracting the time-varying aerodynamic load to completing one bidirectional fluid-structure interaction (FSI) iterative calculation, until the convergence criterion is met or the maximum number of iterations within a substep is reached. Once the calculation of the coupled time substep converges, the calculation process advances to the next coupled time substep, repeating the steps from extracting the time-varying aerodynamic load to completing one bidirectional FSI iterative calculation, until all coupled time substeps are completed.

[0039] In practical implementation, the dynamic displacement field of the blades is fed back as the dynamic boundary conditions of the three-dimensional unsteady steam compressible flow model through a two-way real-time data exchange interface, thereby updating the shape and position of the computational mesh in the steam flow region. The two-way real-time data exchange interface also transmits the dynamic displacement field of the blades to the dynamic mesh module of the computational fluid dynamics solver. Based on the transmitted displacement data, the dynamic mesh module uses a combination of spring approximation smoothing and local mesh re-division to drive the position updates of approximately twelve million mesh nodes within the fluid computational domain. In the region near the blade surface, mesh deformation strictly follows the displacement amount given by the dynamic displacement field. Within the fluid region more than five times the blade height from the blade wall, the boundary displacement is smoothly transmitted to the internal mesh nodes using the spring approximation smoothing method. The stiffness distribution of the virtual spring follows the following formula:

[0040] in: Indicates the connection node With nodes The stiffness coefficient of the virtual spring, The mesh deformation stiffness coefficient is a constant related to the material's elastic modulus and the characteristic area of ​​the mesh. Represents a node coordinate vector, Represents a node coordinate vector, This is a small constant to prevent the denominator from being zero. When the mass of a local mesh element falls below a preset threshold of 0.3 due to deformation, local mesh remapping is triggered. After the mesh update, the three-dimensional unsteady steam compressible flow model, based on the new mesh shape and position, performs the steam flow field calculation in the next coupling time substep. The steps from extracting time-varying aerodynamic loads to completing one bidirectional fluid-structure interaction iteration are repeated until both the dynamic displacement field and the steam flow field of the blade reach the preset convergence criteria. Within each coupling time substep, after completing one bidirectional data exchange and their respective solutions, the increment norms of key physical quantities of the dynamic displacement field and the steam flow field are calculated, and the flow field convergence criterion and the structural field convergence criterion are defined. The flow field convergence criterion is that the absolute value of the average pressure fluctuation rate on the blade surface is less than the first threshold of 0.5%, and the structural field convergence criterion is that the rate of change of the maximum dynamic strain energy of the blade is less than the second threshold of 1.0%. During the iteration process of each coupling time substep, simultaneously... The average pressure fluctuation rate on the blade surface and the rate of change of the maximum dynamic strain energy of the blade are monitored. When the average pressure fluctuation rate on the blade surface and the rate of change of the maximum dynamic strain energy of the blade simultaneously satisfy the flow field convergence criterion and the structural field convergence criterion, the coupling calculation within the coupling time substep is determined to have converged. If the convergence criterion is not met, the steps from extracting the time-varying aerodynamic load to completing one bidirectional fluid-structure interaction iteration calculation are continued within the same coupling time substep. The substep iteration is performed until the convergence criterion is met or the maximum number of iterations within the substep is reached (5). When the calculation of the coupling time substep has converged, the calculation process proceeds to the next coupling time substep.

[0041] In some embodiments, the local mesh refactoring process monitors the quality changes of mesh cells within a specific region. Referring to Table 2, the triggering and results of local region mesh refactoring within a coupled time substep are shown: Table 2: Local Mesh Element Quality Monitoring and Refactoring Record Table

[0042] It is understandable that the spring approximation smoothing method adjusts the stiffness coefficient of the virtual spring. To control the gradient of mesh deformation propagation, closer mesh nodes have a larger spring stiffness coefficient, resulting in stronger deformation compatibility. Optionally, the mesh deformation stiffness coefficient in the formula... The mesh size can be set based on the product of the blade material's elastic modulus and the average area of ​​the mesh elements on the blade's wetted surface. Local mesh refactoring serves as a safety net mechanism, directly reconstructing the local mesh to maintain computational reliability when mesh distortion is severe. This can be understood as the average pressure on the blade surface in the flow field convergence criterion. Its volatility is calculated from the arithmetic mean of all pressure probe data on the monitoring surface. The calculation formula is:

[0043] Where: the superscript n represents the iteration step within the current substep, and the maximum dynamic strain energy of the blade in the structural field convergence criterion. The rate of change is read directly from the energy output file of the structure solver. The calculation formula is: Setting an upper limit on the number of iterations within a substep is to prevent the solution process from looping infinitely in extremely nonlinear cases. When the maximum number of iterations is reached and convergence is still not achieved, the system will record a warning message and use the result of the last iteration to enter the next coupled time substep, so as to ensure the continuous progress of the computation process.

[0044] In one embodiment of the present invention, the dynamic displacement field of the blade is coupled and iteratively calculated to obtain the coupled simulation results of the blade. This includes: feeding back the dynamic displacement field of the blade as the dynamic boundary conditions of the three-dimensional unsteady steam compressible flow model through the two-way real-time data exchange interface, thereby updating the shape and position of the computational grid in the steam flow region and completing one two-way fluid-structure interaction iterative calculation. The steps from extracting the time-varying aerodynamic load to completing one two-way fluid-structure interaction iterative calculation are repeated until both the dynamic displacement field of the blade and the steam flow field reach the preset convergence criteria, and the coupled simulation results in the converged state are obtained. Based on the coupled simulation results in the converged state, the aerodynamic damping characteristics, dynamic stress distribution, and flutter stability boundary of the blade in the target wide load range are analyzed.

[0045] Based on the coupled simulation results under the convergent state, the aerodynamic damping characteristics, dynamic stress distribution, and flutter stability boundary of the blade within the target wide load range are analyzed. This includes: extracting time-domain response data of the blade at multiple typical load steady-state operating points from the coupled simulation results under the convergent state; performing Fourier transform on the time-domain response data at each operating point to identify the dominant frequency and mode shape of the blade vibration; quantifying the aerodynamic damping characteristics by calculating the sign and magnitude of the work done by the aerodynamic force on the blade within one vibration cycle at the dominant frequency; extracting the equivalent stress time history of each blade element throughout the coupled simulation time from the solution results of the finite element structural dynamics model, and statistically obtaining the dynamic stress distribution, including the maximum dynamic stress value and its location; simulating different loads by systematically changing the inlet flow rate or back pressure parameters, repeating the coupled simulation process, and recording the critical operating point where the blade vibration response changes from stable to divergent; summarizing the vibration stability data under different loads, plotting the curve of blade amplitude changing with load, and identifying the load point where the amplitude begins to increase sharply as the flutter stability boundary.

[0046] In specific implementation, the dynamic displacement field of the blade is coupled and iteratively calculated to obtain the coupled simulation results of the blade. This process includes feeding back the dynamic displacement field of the blade as the dynamic boundary conditions of the three-dimensional unsteady steam compressible flow model through a two-way real-time data exchange interface, thereby updating the shape and position of the computational grid in the steam flow region, completing one two-way fluid-structure interaction iterative calculation, and repeating the steps from extracting time-varying aerodynamic loads to completing one two-way fluid-structure interaction iterative calculation until both the dynamic displacement field of the blade and the steam flow field reach the preset convergence criteria, and obtaining the coupled simulation results under the convergence state. The convergence criteria are that the absolute value of the average pressure fluctuation rate on the blade surface is less than 0.5% and the rate of change of the maximum dynamic strain energy of the blade is less than 1.0%. Based on the coupled simulation results under the convergence state, the aerodynamic damping characteristics, dynamic stress distribution, and flutter stability boundary of the blade in the target wide load range are analyzed.

[0047] In some embodiments, the aerodynamic damping characteristics, dynamic stress distribution, and flutter stability boundary of the blade within the target wide load range are analyzed based on the coupled simulation results under convergent conditions. Specifically, the time-domain response data of the blade at four typical steady-state operating points (30%, 50%, 75%, and 100% rated load) are extracted from the coupled simulation results under convergent conditions. The data sampling time for each operating point is 0.02 seconds. Fourier transform is performed on the time-domain response data for each operating point to identify the dominant frequency and mode shape of the blade vibration. For example, under 75% load, the first-order bending mode shape is identified as dominant, with a frequency of 112 Hz. At the dominant frequency, the aerodynamic damping characteristics are quantified by calculating the sign and magnitude of the work done by the aerodynamic force on the blade within one vibration cycle. The calculation formula is:

[0048] in: This represents the work done by aerodynamic forces on the blade during one vibration cycle. Indicates the period of oscillation. This represents the time-varying aerodynamic force vector acting on the wetted surface of the blade. This represents the vibration velocity vector at a corresponding point on the blade surface, integrated over one complete vibration cycle. The simulation is conducted internally. From the solution results of the finite element structural dynamics model, the equivalent stress time history of each blade element throughout the entire coupled simulation time is extracted. The dynamic stress distribution is statistically obtained, including the maximum dynamic stress value and its location. For example, the maximum dynamic stress is 285 MPa, located in the upper part of the transition region between the blade body and the tenon. Different loads are simulated by systematically changing the inlet flow rate or back pressure parameters. The complete coupled simulation process is repeated, recording the critical operating point where the blade vibration response changes from stable to divergent. For example, when the load is reduced to 28% of the rated load, the blade amplitude increases by more than 10% within one simulation cycle. Vibration stability data under different loads are summarized, and the curve of the maximum amplitude at the blade tip as a function of load is plotted. The load point where the amplitude begins to increase sharply is identified as the flutter stability boundary.

[0049] In practical implementation, the process of repeatedly executing the steps from extracting time-varying aerodynamic loads to completing one bidirectional fluid-structure interaction iterative calculation is an automated loop controlled by a bidirectional real-time data exchange interface. Within a typical coupling time substep, if the convergence criterion is not met, the interface will re-extract the time-varying aerodynamic loads from the updated three-dimensional unsteady vapor compressible flow model and transfer them until convergence is achieved within the substep or the maximum number of iterations is reached. Optionally, when performing Fourier transform on the time-domain response data, a Fast Fourier Transform algorithm with a Hanning window is used to reduce spectral leakage. The equivalent stress time history extracted from the finite element structural dynamics model is statistically processed by calculating the maximum, minimum, average, and standard deviation of stress for each element throughout the entire time history, and outputting the dynamic stress distribution in the form of a contour plot. It can be understood that the formula... Calculated work A negative value indicates that the aerodynamic damping is positive, and the system dissipates energy through vibration; work When the value is positive, it indicates that the aerodynamic damping is negative, and the system absorbs energy from the airflow, which may lead to flutter. It can be understood that when plotting the curve of blade amplitude versus load, the horizontal axis represents the normalized load, the vertical axis represents the normalized tip amplitude, and the flutter stability boundary corresponds to the load value at the inflection point where the slope of the curve increases significantly.

[0050] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for aerodynamic-structural coupled simulation design of turbine blades under wide loads, characterized in that, The method includes: Based on the initial geometric configuration of the turbine blades, a three-dimensional unsteady steam compressible flow model of the blade passage is established in the computational fluid dynamics solver. The three-dimensional unsteady steam compressible flow model is used to simulate strong unsteady steam excitation under a wide load range. A finite element structural dynamics model of the blade and the disk is established in the structural dynamics solver. The finite element structural dynamics model takes into account the contact nonlinearity and material nonlinearity at the blade root connection. Construct a bidirectional real-time data exchange interface connecting the computational fluid dynamics solver and the structural dynamics solver; Under the action of the bidirectional real-time data exchange interface, the time-varying aerodynamic loads acting on the wet surface are extracted from the three-dimensional unsteady steam compressible flow model, and the time-varying aerodynamic loads are mapped to the nodal force boundary conditions on the finite element structural dynamics model. The finite element structural dynamic model is driven to solve the transient dynamic response of the blade under the nodal force boundary conditions to obtain the dynamic displacement field of the blade; The dynamic displacement field of the blade is calculated using a coupled iterative method to obtain the coupled simulation results of the blade.

2. The aerodynamic-structural coupled simulation design method for wide-load turbine blades according to claim 1, characterized in that, The establishment of a three-dimensional unsteady steam compressible flow model for the blade passage in the computational fluid dynamics solver includes: Based on the geometric shape of the turbine blades and adjacent stator blades, the fluid computation domain of the blade passage is extracted. The fluid computation domain includes the main channel, the blade tip clearance region, and the near-wall boundary layer region. The fluid computational domain is divided into unstructured hybrid meshes, and the boundary layer mesh is refined in key areas of the blade surface and endwall to generate a computational mesh system suitable for solving unsteady flows. The physical properties of the steam working fluid are defined by adopting the equation of state and transport coefficient model applicable to the actual physical properties of steam. Set the inlet total pressure, total temperature boundary conditions and outlet static pressure boundary conditions corresponding to the wide load operating range, and specify the treatment method for the dynamic and static blade interface. A large eddy simulation turbulence model based on scale-adaptive simulation was selected, and combined with dynamic mesh technology, to establish a three-dimensional unsteady steam compressible flow model capable of simulating the entire process from startup, variable load to deep peak shaving.

3. The aerodynamic-structural coupled simulation design method for wide-load turbine blades according to claim 1, characterized in that, The establishment of the finite element structural dynamics model of the blade and disk in the structural dynamics solver includes: Based on the solid geometric model of the blade, high-order hexahedral elements are used to mesh the blade solid, and local mesh refinement is performed in the transition area between the blade body and the tenon and in the stress concentration area of ​​the pull hole. The wheel disk is simplified in modeling, while the rim part connected to the blade tenon is retained. The mesh is generated using a mixture of tetrahedral and hexahedral elements. In the finite element preprocessing, the nonlinear constitutive relations of the blade and disk materials are defined. The nonlinear constitutive relations include the elastic modulus, yield strength and cyclic plastic hardening parameters that vary with temperature. Set up the contact pair between the leaf root tenon and the wheel disk tenon, and define the friction coefficient and contact algorithm parameters to simulate the contact nonlinearity; Apply a rotational speed constraint to the center of the wheel and constrain the radial and axial displacements of the inner surface of the wheel. After assigning material properties, setting constraints and loads, the finite element structural dynamic model is formed, which prepares for solving transient dynamic response.

4. The aerodynamic-structural coupled simulation design method for wide-load turbine blades according to claim 1, characterized in that, Constructing a bidirectional real-time data exchange interface connecting the computational fluid dynamics solver and the structural dynamics solver includes: Set the time step for the coupling analysis and divide the total time of the coupling analysis into multiple coupling time substeps; At the beginning of each coupled time substep, the bidirectional real-time data exchange interface receives the pressure distribution and shear stress distribution of the wetted surface of the blade under the current steam flow field from the computational fluid dynamics solver. The pressure distribution and shear stress distribution together constitute the time-varying aerodynamic load. The loosely coupled partitioning algorithm is invoked to conservely interpolate the time-varying aerodynamic load from the fluid mesh nodes of the computational fluid dynamics solver to the structural finite element mesh nodes of the structural dynamics solver, thereby generating the nodal force boundary conditions. After the structural dynamics solver completes the transient dynamic response solution within the current coupled time substep, the bidirectional real-time data exchange interface receives the dynamic displacement field characterizing the blade deformation and motion from the structural dynamics solver. The loosely coupled partitioning algorithm is invoked again to transfer the dynamic displacement field from the structural finite element mesh node of the structural dynamics solver to the fluid mesh node of the computational fluid dynamics solver, driving the fluid computational mesh to perform corresponding deformation and motion. After completing the bidirectional transfer of the time-varying aerodynamic load and the dynamic displacement field, the bidirectional real-time data exchange interface sends a synchronization signal to the computational fluid dynamics solver and the structural dynamics solver, enabling the computational fluid dynamics solver and the structural dynamics solver to enter the next coupled time substep of calculation.

5. The aerodynamic-structural coupling simulation design method for wide-load turbine blades according to claim 4, characterized in that, The working principle of the loosely coupled partitioning algorithm is as follows: During the initialization phase, a spatial positional mapping between the two sets of mesh nodes is established based on the fluid mesh of the computational fluid dynamics solver and the structural finite element mesh of the structural dynamics solver. Calculate the overlap area weighting coefficient between the fluid mesh surface element and the structural finite element surface element, and combine the overlap area weighting coefficient with the element shape function to construct the load transfer matrix from the fluid mesh node to the structural mesh node; By utilizing the principle of conservation interpolation, the aerodynamic load vector on the fluid grid node is multiplied by the load transfer matrix to obtain the equivalent nodal force acting on the structural grid node, ensuring the global conservation of force and torque during the transfer process. In the displacement transfer process from the structural mesh to the fluid mesh, a displacement transfer matrix is ​​constructed based on the radial basis function interpolation method. The radial basis function interpolation method uses the displacement of the structural mesh nodes as known quantities and obtains the displacement of the fluid mesh boundary nodes by solving the linear system. Within each coupling time substep, the load transfer matrix and the displacement transfer matrix are queried to achieve fast interpolation and exchange of data. At the end of each coupling time step, the energy conservation error of the transferred data is monitored and corrected to ensure the numerical stability of the bidirectional coupling solution.

6. The aerodynamic-structural coupled simulation design method for wide-load turbine blades according to claim 1, characterized in that, The process of driving the finite element structural dynamics model to solve the transient dynamic response of the blade under the nodal force boundary conditions includes: In the structural dynamics solver, initial conditions are set for the finite element structural dynamics model, including that the initial displacement field and initial velocity field of the blade are both zero. In the transient solver, an implicit time integration algorithm is selected, and a calculation time step consistent with the time step of the coupled analysis is set. Within each coupling time substep, the nodal force boundary conditions transmitted from the bidirectional real-time data exchange interface are applied to the corresponding nodes on the blade surface. Considering the material nonlinearity and the contact nonlinearity, the nonlinear dynamic equilibrium equation is solved iteratively within the calculation time step to obtain the displacement, velocity and acceleration of each node of the blade at the end of the current coupling time substep; The results of each time step are accumulated to obtain the time history response of the blade during the entire coupled simulation time. The time history response is the dynamic displacement field.

7. The aerodynamic-structural coupled simulation design method for wide-load turbine blades according to claim 1, characterized in that, The dynamic displacement field of the blade is calculated using a coupled iterative method to obtain the coupled simulation results of the blade, including: Through the bidirectional real-time data exchange interface, the dynamic displacement field of the blade is fed back as the dynamic boundary condition of the three-dimensional unsteady steam compressible flow model, thereby updating the shape and position of the computational grid in the steam flow region and completing a bidirectional fluid-structure interaction iterative calculation. Repeat the steps from extracting time-varying aerodynamic loads to completing one bidirectional fluid-structure interaction iterative calculation until the dynamic displacement field and steam flow field of the blade both reach the preset convergence criteria, and obtain the coupled simulation results under the convergence state. Based on the coupled simulation results under the convergence state, the aerodynamic damping characteristics, dynamic stress distribution, and flutter stability boundary of the blade are analyzed in the target wide load range.

8. The aerodynamic-structural coupling simulation design method for wide-load turbine blades according to claim 7, characterized in that, Through the bidirectional real-time data exchange interface, the dynamic displacement field of the blades is fed back as the dynamic boundary conditions of the three-dimensional unsteady steam compressible flow model, thereby updating the shape and position of the computational mesh in the steam flow region, including: The bidirectional real-time data exchange interface transmits the dynamic displacement field of the blade to the dynamic mesh module of the computational fluid dynamics solver. The dynamic mesh module updates the position of the mesh nodes in the fluid computational domain by using a combination of spring approximation smoothing and local mesh re-subdivision based on the transmitted displacement data. In the region near the blade surface, the mesh deformation strictly follows the displacement amount given by the dynamic displacement field, ensuring the consistency of the fluid-solid interface geometry; In the fluid region far from the blade wall, the boundary displacement is smoothly transferred to the internal mesh nodes by the spring approximation smoothing method to prevent mesh distortion; When the quality of a local mesh cell falls below a preset threshold due to deformation, the local mesh is re-divided, and a new high-quality mesh is automatically generated in the local area with excessive deformation. After the mesh update is completed, the three-dimensional unsteady steam compressible flow model performs steam flow field calculations in the next coupled time substep based on the new mesh shape and position.

9. The aerodynamic-structural coupling simulation design method for wide-load turbine blades according to claim 8, characterized in that, The repeated execution of the steps from extracting the time-varying aerodynamic load to completing one bidirectional fluid-structure interaction iterative calculation, until both the dynamic displacement field and the steam flow field of the blade reach the preset convergence criteria, includes: Within each coupled time substep, after completing one bidirectional data exchange and each solution, the incremental norm of the key physical quantities of the dynamic displacement field and the steam flow field is calculated. Define flow field convergence criteria and structural field convergence criteria. The flow field convergence criteria is that the absolute value of the average pressure fluctuation rate on the blade surface is less than a first threshold, and the structural field convergence criteria is that the rate of change of the maximum dynamic strain energy of the blade is less than a second threshold. During the iteration of each coupling time substep, the average pressure fluctuation rate on the blade surface and the rate of change of the maximum dynamic strain energy of the blade are monitored simultaneously. When the average pressure fluctuation rate on the blade surface and the rate of change of the maximum dynamic strain energy of the blade simultaneously satisfy the flow field convergence criterion and the structural field convergence criterion, the coupling calculation within the coupling time substep is determined to have converged. If the convergence criterion is not met, the steps from extracting the time-varying aerodynamic load to completing one bidirectional fluid-structure interaction iterative calculation will continue to be executed within the same coupling time substep, and the substep iteration will be performed until the convergence criterion is met or the maximum number of substep iterations is reached. Once the calculation of the coupled time substep has converged, the calculation process proceeds to the next coupled time substep, repeating the steps from extracting the time-varying aerodynamic load to completing one bidirectional fluid-structure interaction iterative calculation, until all coupled time substeps have been calculated.

10. The aerodynamic-structural coupled simulation design method for wide-load turbine blades according to claim 7, characterized in that, Based on the coupled simulation results under the convergent state, the aerodynamic damping characteristics, dynamic stress distribution, and flutter stability boundary of the blade in the target wide load range are analyzed, including: From the coupled simulation results under the convergence state, extract the time-domain response data of the blades under multiple typical load steady-state operating conditions; Fourier transform is performed on the time-domain response data at each operating point to identify the dominant frequency and mode shape of blade vibration; At the dominant frequency, the aerodynamic damping characteristics are quantified by calculating the sign and magnitude of the work done by the aerodynamic force on the blade within one vibration cycle. From the solution results of the finite element structural dynamic model, the equivalent stress time history of each blade element during the entire coupled simulation time is extracted, and the dynamic stress distribution is statistically obtained, including the maximum dynamic stress value and its location. By systematically changing the inlet flow rate or back pressure parameters to simulate different loads, and repeatedly coupling the simulation process, the critical operating point of the blade vibration response from steady to divergent is recorded. By summarizing vibration stability data under different loads, a curve of blade amplitude changing with load is plotted, and the load point where the amplitude begins to increase sharply is identified as the flutter stability boundary.

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