A method for determining the aerodynamic damping of forced vibration of blades under whole-machine conditions

Abstract

This invention relates to the field of simulation computing technology and discloses a method for determining the aerodynamic damping of forced vibration of blades under a whole-machine environment. The method acquires the whole-machine layout data and target vibration frequency data of the target blade row, identifies components affecting aerodynamic damping, and generates a component list. Based on the component list, a fluid computational domain is established, and a first computational model where all blades are stationary and a second computational model referencing only blade vibration are established. Unsteady aerodynamic force calculations are performed on the two computational models to obtain the aerodynamic excitation force and the combined aerodynamic force. The damping aerodynamic force is obtained by subtraction, and the damping aerodynamic force influence coefficient is obtained. Phase superposition is performed based on a specified nodal diameter (ND) to obtain the complex Fourier coefficients of the superimposed damping aerodynamic force under the specified ND, and the aerodynamic damping is calculated. This invention reduces the number of aerodynamic damping calculations under different NDs and improves the adaptability of the calculation results to the whole-machine environment by modeling the whole-machine environment, separating force terms, and superimposing the influence coefficients.

Description

Technical Field

[0001] This invention relates to the field of simulation calculation technology, specifically to a method for determining the aerodynamic damping of forced vibration of blades under whole-machine conditions. Background Technology

[0002] Currently, in the forced vibration analysis of aero-engines, gas turbines, and axial-flow turbomachinery, aerodynamic damping is a crucial input parameter for determining blade vibration response. The target blade row is located within the overall flow channel, and its aerodynamic forces are not only related to its own airfoil, vibration mode, and target vibration frequency, but also influenced by the upstream and downstream blade rows, casing boundaries, hub boundaries, and the rotor-stator interface. Unsteady pressure disturbances induced by blade vibration propagate within the flow channel and can produce reflection, scattering, or coupling effects at adjacent structures. Therefore, the aerodynamic damping for different nodal diameters (ND) needs to be determined in conjunction with the overall system environment.

[0003] Regarding the aforementioned issues, existing aerodynamic damping calculations typically select the target blade row or its adjacent flow channels as the calculation object. The phase relationship between the blades is set according to the nodal diameter (ND) to be analyzed, and a given vibration mode and amplitude are applied to the blades. During the calculation, the time history of blade surface pressure, shear stress, or integral aerodynamic force is obtained through three-dimensional unsteady CFD calculations. Then, the aerodynamic work within one vibration cycle is calculated in conjunction with the blade vibration velocity, thereby obtaining the aerodynamic damping under the corresponding nodal diameter (ND). For multiple nodal diameters (ND), it is usually necessary to set the corresponding phase state separately and repeat the calculation.

[0004] Existing methods still have shortcomings when dealing with the overall system environment and multi-node diameter calculations. If the computational domain only includes the target blade row, it is easy to ignore the influence of upstream structure, downstream structure, and rotor-stator interface on unsteady pressure disturbances. If a full-scale three-dimensional unsteady calculation is established for each node diameter (ND), the number of calculations increases with the phase state. On the other hand, in the overall system environment, the aerodynamic excitation force and the damping aerodynamic force induced by blade vibration will be at the same target vibration frequency, and it is difficult to achieve stable separation by relying solely on frequency components. In summary, there is a contradiction between preserving the influence of the overall system environment and reducing the computational load of multiple NDs, and there is a lack of effective means of force term separation. Therefore, this invention provides a method for determining the aerodynamic damping of forced blade vibration in the overall system environment to overcome the shortcomings of the prior art. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for determining the aerodynamic damping of forced vibration of blades under whole-machine environment. This method solves the problem of reducing redundant calculations of aerodynamic damping for different ND diameters and separating damping aerodynamic forces while retaining the influence of the whole-machine environment.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for determining the aerodynamic damping of forced vibration of blades under whole-machine conditions includes the following steps:

[0008] Acquire the overall layout data and target vibration frequency data of the target blade row, identify the components affecting aerodynamic damping and generate a component list; establish a fluid computational domain based on the component list, and establish a first computational model where all blades are stationary and a second computational model that only considers blade vibration; perform unsteady aerodynamic force calculations on the first and second computational models to obtain aerodynamic excitation force and composite aerodynamic force; obtain the damping aerodynamic force by subtracting the composite aerodynamic force from the aerodynamic excitation force; obtain the damping aerodynamic force influence coefficient based on the damping aerodynamic force, perform phase superposition of the damping aerodynamic force influence coefficient based on the specified section diameter ND to obtain the superimposed complex Fourier coefficient of the damping aerodynamic force under the specified ND, and calculate the aerodynamic damping based on the superimposed complex Fourier coefficient of the damping aerodynamic force under the specified ND.

[0009] By adopting the above technical solution, since a first calculation model in which all blades are stationary and a second calculation model that only refers to blade vibration are established in the same whole-machine environment fluid calculation domain, and the damping aerodynamic force is obtained by using the differential relationship between the synthetic aerodynamic force and the aerodynamic excitation force, and the damping aerodynamic force influence coefficient is superimposed according to the specified section diameter ND, it is possible to calculate the aerodynamic damping under different NDs while retaining the aerodynamic influence of the whole-machine environment, thereby reducing the calculation workload of establishing unsteady vibration calculation models for multiple section diameters.

[0010] Preferably, the specific steps for identifying components affecting aerodynamic damping and generating a component list are as follows: Based on the overall machine layout data, determine the target blade row for forced vibration aerodynamic damping analysis; read the blade rows and fixed structure information before and after the target blade row along the airflow direction, as the upstream and downstream structures of the target blade row; based on the target vibration frequency data, the circumferential modal characteristics of the blade row, the local sound velocity, the flow velocity, and the channel geometry, determine the propagation, reflection, scattering, or coupling effects of the upstream and downstream structures on the unsteady pressure disturbance induced by blade vibration; identify the structures with propagation, reflection, scattering, or coupling effects as components affecting aerodynamic damping, and generate the component list.

[0011] By adopting the above technical solution, the range of components that need to be included in the aerodynamic damping analysis can be determined based on the target vibration frequency data and the overall layout data, so that the fluid computation domain covers the upstream and downstream structures that affect the damping aerodynamic forces.

[0012] Preferably, the specific steps for establishing the fluid computational domain based on the component list are as follows: the component list includes at least the target blade row, the upstream influencing component of the target blade row, the downstream influencing component of the target blade row, the casing boundary, and the hub boundary; for cases where different speed ranges are adjacent, a sliding plane is set between the rotor computational domain and the stator computational domain; and in the fluid computational domain, an inlet boundary, an outlet boundary, a periodic boundary, a wall boundary, and a sliding plane boundary are set.

[0013] By adopting the above technical solution, the target blade row, upstream and downstream influencing components and the boundary relationship between rotor and stator can be preserved in the fluid computation domain, so that the computation model can reflect the boundary constraints and unsteady flow field transmission relationship under the whole machine environment.

[0014] Preferably, the specific steps for establishing a first calculation model in which all blades are stationary and a second calculation model that only references blade vibration are as follows: establishing the first calculation model and the second calculation model based on the same fluid calculation domain; in the first calculation model, ensuring that no vibration displacement is applied to any blade in the target blade row; in the second calculation model, applying a given vibration mode and a given vibration mode coordinate amplitude only to the reference blade, and ensuring that no vibration displacement is applied to the remaining blades in the target blade row.

[0015] By adopting the above technical solution, the first calculation model is used to obtain the aerodynamic excitation force under the whole machine environment, and the second calculation model is used to obtain the composite aerodynamic force after the superposition of the aerodynamic excitation force and the damping aerodynamic force induced by the vibration of the reference blade, so that the damping aerodynamic force can be obtained by the aerodynamic force difference under the same blade number.

[0016] Preferably, the specific steps for performing unsteady aerodynamic calculations on the first and second calculation models are as follows: when using the time-domain full-circumference calculation method, a target blade full-circumference model is established and three-dimensional unsteady calculations are performed to output the aerodynamic time history of each blade; or the frequency-domain harmonic method is used to calculate the harmonic order corresponding to the target vibration frequency, and the complex Fourier coefficients corresponding to each blade are directly output at the specified harmonic frequency; wherein, the first and second calculation models use the same fluid boundary conditions, the same fluid property parameters, the same mesh topology, and the same target vibration frequency.

[0017] By adopting the above technical solutions, both the time-domain full-cycle calculation method and the frequency-domain harmonic method can output aerodynamic information at the target vibration frequency, and the aerodynamic results of the first calculation model and the second calculation model are comparable by using the same calculation conditions.

[0018] Preferably, the specific steps for obtaining the aerodynamic excitation force and the composite aerodynamic force are as follows: performing unsteady aerodynamic force calculations on the first calculation model, recording the aerodynamic force results of each blade under the condition that all blades are stationary, and using the aerodynamic force results of each blade under the condition that all blades are stationary as the aerodynamic excitation force; performing unsteady aerodynamic force calculations on the second calculation model, recording the aerodynamic force results of each blade under the condition that only the blades are vibrating, and using the aerodynamic force results of each blade under the condition that only the blades are vibrating as the composite aerodynamic force; the aerodynamic excitation force and the composite aerodynamic force have the same blade number, the same target vibration frequency, and the same data sampling interval.

[0019] By adopting the above technical solution, the aerodynamic excitation force and the combined aerodynamic force are kept consistent in terms of blade number, target vibration frequency and data sampling interval, which facilitates the differential processing of the aerodynamic results at the same blade position.

[0020] Preferably, the specific steps for obtaining the damping aerodynamic force by subtracting the synthetic aerodynamic force from the aerodynamic excitation force are as follows: read the synthetic aerodynamic force of the corresponding blade in the second calculation model; read the aerodynamic excitation force of the same blade in the first calculation model; under the same blade number, the same target vibration frequency, and the same data sampling interval, subtract the aerodynamic excitation force from the synthetic aerodynamic force to obtain the damping aerodynamic force of the corresponding blade; repeat the above process for each blade involved in the influence coefficient identification.

[0021] By adopting the above technical solution, the damping aerodynamic force induced by the vibration of the reference blade can be separated from the synthetic aerodynamic force, avoiding the need to rely solely on frequency screening to distinguish between aerodynamic excitation force and damping aerodynamic force.

[0022] Preferably, the specific steps for obtaining the damping aerodynamic influence coefficient based on the damping aerodynamic force are as follows: when the unsteady aerodynamic force calculation adopts the time-domain full-cycle calculation method, Fourier transform is performed on the time history of the damping aerodynamic force of each blade to obtain the complex Fourier coefficient of the damping aerodynamic force at the target vibration frequency; when the unsteady aerodynamic force calculation adopts the frequency-domain harmonic method, the complex Fourier coefficient output by the second calculation model is directly subtracted from the complex Fourier coefficient output by the first calculation model; the obtained complex Fourier coefficient is used as the damping aerodynamic influence coefficient corresponding to each blade.

[0023] By adopting the above technical solution, the damping aerodynamic force of each blade can be uniformly converted into complex Fourier coefficients at the target vibration frequency, so that the damping aerodynamic force influence coefficient contains both amplitude and phase information.

[0024] Preferably, the specific steps for performing phase superposition of the damping aerodynamic influence coefficients based on the specified section diameter ND to obtain the superimposed damping aerodynamic complex Fourier coefficients under the specified ND are as follows: reading the total number of blades in the target blade row and the specified section diameter ND; determining the phase angle between adjacent blades in the specified ND vibration mode based on the total number of blades and the specified section diameter ND; using the reference blade as the phase reference, converting the damping aerodynamic influence coefficients corresponding to different blade numbers to the reference blade phase reference; summing the damping aerodynamic influence coefficients converted to the reference blade phase reference to obtain the superimposed damping aerodynamic complex Fourier coefficients under the specified ND.

[0025] By adopting the above technical solution, the damping aerodynamic influence coefficients of different blade numbers can be superimposed according to the circumferential phase distribution corresponding to the specified section diameter ND, so that the single influence coefficient extraction result can be used for aerodynamic damping calculation under multiple NDs.

[0026] Preferably, the specific steps for calculating aerodynamic damping based on the superimposed complex Fourier coefficients of the damping aerodynamic force under the specified ND are as follows: constructing a time history of the damping aerodynamic force based on the superimposed complex Fourier coefficients of the damping aerodynamic force under the specified ND, or directly using the Fourier coefficients at the target vibration frequency; constructing a time history of the vibration displacement and a time history of the vibration velocity of the reference blade based on the blade vibration circular frequency and the given vibration mode coordinate amplitude, or constructing a Fourier representation of the vibration displacement and vibration velocity of the reference blade; multiplying the time history of the damping aerodynamic force by the time history of the vibration velocity and integrating it over one vibration cycle to obtain the work done by the damping aerodynamic force over one vibration cycle; calculating the aerodynamic damping under the specified ND based on the work done by the damping aerodynamic force over one vibration cycle, the blade vibration circular frequency, and the given vibration mode coordinate amplitude.

[0027] By adopting the above technical solution, the complex Fourier coefficients of the damping aerodynamic force superimposed under a specified ND can be converted into periodic work, and the aerodynamic damping under the corresponding ND can be obtained according to the periodic work, the blade vibration circular frequency and the given vibration mode coordinate amplitude.

[0028] This invention provides a method for determining the aerodynamic damping of forced vibration of blades under whole-machine conditions. It has the following beneficial effects:

[0029] 1. This invention identifies the upstream and downstream structures, casing boundaries, hub boundaries, and rotor-stator interface relationships that affect aerodynamic damping within the overall machine environment through a parts list. Based on this, a fluid computational domain is established, enabling the aerodynamic damping calculation process to retain the influence of the overall machine environment on the target blade row. Compared to methods that only calculate for a single blade row, this method can reflect the propagation, reflection, scattering, or coupling effects of unsteady pressure disturbances between adjacent structures, improving the correspondence between the aerodynamic damping calculation results and the overall machine operating state.

[0030] 2. This invention establishes a first calculation model where all blades are stationary and a second calculation model that only considers blade vibration. The damping aerodynamic force is obtained by subtracting the synthetic aerodynamic force from the aerodynamic excitation force. This method allows the aerodynamic excitation force at the target vibration frequency and the damping aerodynamic force induced by blade vibration to be separated under the same blade number, the same target vibration frequency, and the same data sampling interval. This avoids relying solely on frequency filtering to distinguish force terms and facilitates obtaining the damping aerodynamic force influence coefficient corresponding to each blade.

[0031] 3. This invention performs phase superposition of the damping aerodynamic influence coefficients according to the inter-blade phase angle corresponding to a specified nodal diameter (ND), obtaining the superimposed complex Fourier coefficients of the damping aerodynamic forces under the specified ND, and further calculates the corresponding aerodynamic damping. Through this processing, the calculation results of the first and second calculation models can be used for aerodynamic damping calculations under multiple NDs, reducing the number of full-scale three-dimensional unsteady calculations for different nodal diameters, and improving the engineering applicability of aerodynamic damping assessment for forced vibration of blades under whole-machine environment. Attached Figure Description

[0032] Figure 1 This is a system architecture diagram of the present invention;

[0033] Figure 2 This is a schematic diagram of the overall machine environment blade arrangement analysis model of the present invention;

[0034] Figure 3 This is a schematic diagram of a vibrating blade specified in the frequency domain harmonic method of the present invention;

[0035] Figure 4 This is a general flowchart of the method of the present invention;

[0036] Figure 5 This is a flowchart illustrating the identification of components affecting aerodynamic damping according to the present invention.

[0037] Figure 6 This is a flowchart illustrating the construction process of the whole-system environment CFD calculation model of the present invention;

[0038] Figure 7 This is a flowchart illustrating the separation of excitation and damping forces in this invention.

[0039] Figure 8 This is a flowchart illustrating the aerodynamic damping calculation for different section diameters according to the present invention.

[0040] Figure 9 The graph shows the aerodynamic damping calculation results for different section diameters in a specific application embodiment of the present invention.

[0041] Among them, 1. Inlet guide vane; 2. Rotor blade row; 3. Stator blade row; 4. Vibrating blade; 5. Outlet boundary; 6. Inlet boundary; 7. Periodic boundary. Detailed Implementation

[0042] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] See attached document Figure 1 This invention provides a system for determining the aerodynamic damping of forced vibration of blades under whole-machine environment. The system includes a component identification module, a model construction module, an unsteady simulation module, a force term separation module, and a damping calculation module. Each module sequentially transmits the calculation object, calculation domain, aerodynamic force results, damping force results, and aerodynamic damping results. Based on the characteristic that aerodynamic excitation force and damping aerodynamic force can be linearly superimposed under small amplitude vibration conditions, the system obtains the damping aerodynamic force induced by blade vibration by subtracting the calculation results of all blades in static state from the calculation results of a single reference blade in vibration state. Then, based on the superposition of influence coefficients, the aerodynamic damping under different nodal diameters (ND) is obtained.

[0044] The component identification module is used to determine the range of components in the overall machine environment that need to be included in the aerodynamic damping analysis. The module receives overall machine layout data of the target blade row, relative position data of the blade rows, flow direction data, and target vibration frequency data, and outputs a list of components affecting aerodynamic damping. Components affecting aerodynamic damping include inlet guide vanes, upstream blade rows, downstream blade rows, support plates, measurement probes, local structures of the casing, and local structures of the hub.

[0045] The component identification module analyzes the propagation relationship of unsteady pressure disturbances induced by blade vibration in the axial, circumferential, and radial directions based on the upstream and downstream structures of the target blade row. Components that can alter the amplitude, phase, or boundary reflection conditions of the unsteady pressure disturbances are identified as components affecting aerodynamic damping. The component list output by this module serves as the basis for subsequent computational fluid dynamics (CFD) modeling.

[0046] The model building module is used to establish a CFD calculation model of the entire machine environment based on the component list output by the component identification module. The model building module generates a fluid computation domain for unsteady calculations based on the relative axial position, circumferential channel number, and rotor-stator interface position of the target blade row and its upstream and downstream influencing components.

[0047] See attached document Figure 2 The inlet guide vane 1 is arranged upstream of the target blade row to change the flow direction before entering the target blade row; the rotor blade row 2 is the target blade row for forced vibration aerodynamic damping analysis; the stator blade row 3 is arranged downstream of the rotor blade row 2 to reflect the influence of the downstream blade row on the aerodynamic damping of the target blade row. Figure 2 The coordinate system in the figure is only used to indicate the direction of the calculation model and is not used as an object for the attached figure numbering.

[0048] The model building module establishes two types of computational models. The first type is a model where all blades are stationary; this model is used to obtain the aerodynamic excitation forces generated by the upstream and downstream blade rows and other obstacle structures under whole-machine conditions. The second type is a model that only considers blades vibrating in a given mode; this model is used to obtain the combined aerodynamic force resulting from the superposition of the aerodynamic excitation forces and the damping aerodynamic forces induced by blade vibration. Both types of models use the same fluid boundary conditions, the same fluid property parameters, the same mesh topology, and the same target vibration frequency.

[0049] The unsteady simulation module is used to perform unsteady aerodynamic calculations on the two types of CFD calculation models generated by the model building module. The unsteady simulation module can employ both time-domain full-circumference calculation methods and frequency-domain harmonic methods. The time-domain full-circumference calculation method performs unsteady calculations on the complete circumferential blade row, outputting the aerodynamic results of each blade over time. The frequency-domain harmonic method directly outputs the complex Fourier coefficients corresponding to each blade at the specified harmonic frequency. When using the frequency-domain harmonic method to reduce the number of calculation channels, the target blade row uses a multi-channel calculation domain, while upstream and downstream structures affecting aerodynamic damping use a single-channel or multi-channel calculation domain. (See attached diagram.) Figure 3 When using the frequency domain harmonic method, vibrating blade 4 serves as the reference blade in the second calculation model for applying a given vibration mode and the given vibration mode coordinate amplitude; exit boundary 5 is the boundary for applying the exit conditions of the calculation domain; inlet boundary 6 is the boundary for applying the inlet conditions of the calculation domain; and periodic boundary 7 is the corresponding boundary for the periodic boundary on both sides of the circumference. Vibrating blade 4 is arranged in the middle of the multi-channel calculation domain and is used to extract the damping aerodynamic influence coefficients corresponding to the blade numbers on both sides.

[0050] The force term separation module is used to separate the damping aerodynamic forces induced by blade vibration from the aerodynamic results of two types of computational models. The computational model with all blades stationary outputs the aerodynamic excitation force, while the computational model with reference blade vibration outputs the composite aerodynamic force. The force term separation module subtracts the two types of aerodynamic results according to the same blade number, the same target vibration frequency, and the same data sampling interval to obtain the damping aerodynamic force corresponding to each blade.

[0051] The force term separation module is also used to convert the time history of damping aerodynamic forces into complex Fourier coefficients at the target vibration frequency. For the full-cycle time-domain calculation results, the force term separation module performs a Fourier transform on the time history of damping aerodynamic forces. For the frequency-domain harmonic calculation results, the force term separation module directly subtracts the complex Fourier coefficients output by the two types of calculation models. This yields the damping aerodynamic force influence coefficients corresponding to different blade numbers.

[0052] The damping calculation module is used to calculate aerodynamic damping under different nodal diameters (ND) based on the damping aerodynamic force influence coefficients output by the force term separation module. The module calculates the vibration phase difference between adjacent blades based on the number of blades in the target blade row and the specified nodal diameter, and then performs phase superposition of the damping aerodynamic force contributions of different blades to the reference blade using the influence coefficient method. Based on the superimposed damping aerodynamic force complex Fourier coefficients under the specified ND, the module constructs the damping aerodynamic force time history. Based on the blade vibration angular frequency of the reference blade and the given vibration mode coordinate amplitude, it constructs the vibration displacement time history and vibration velocity time history of the reference blade. It calculates the work done by the damping aerodynamic force on the blade vibration within one vibration cycle, and then calculates the aerodynamic damping based on this work value.

[0053] See attached document Figure 4 This invention provides a method for determining the aerodynamic damping of forced vibration of blades under whole-machine conditions. The method is based on the above-mentioned system and includes the following steps:

[0054] Step S100: Identify the range of components in the overall machine environment that affect aerodynamic damping calculations. This step is performed through the component identification module. This step takes the overall machine layout data of the target blade row, the target blade row data, and the target vibration frequency data as inputs to identify the upstream and downstream structures of the target blade row and generate a list of components that need to be included in the CFD calculation domain.

[0055] Step S200: Establish two types of aerodynamic calculation models that include components affected by the entire machine. This is executed through the model building module. This step establishes the fluid calculation domain based on the component list output in step S100, and establishes a first calculation model where all blades are stationary and a second calculation model that only considers blade vibration.

[0056] Step S300 involves separating the excitation force and damping force using the output results of two types of calculation models. This is performed through the force term separation module. This step extracts unsteady aerodynamic forces from the first and second calculation models and obtains the damping aerodynamic force and its complex Fourier coefficients at the target vibration frequency by subtracting the results from the blades with the same number.

[0057] Step S400: Calculate aerodynamic damping for different section diameters based on the superposition of influence coefficients. This step is executed through the damping calculation module. This step determines the phase angle between blades based on the specified section diameter, performs phase superposition of the damping aerodynamic influence coefficients to obtain the superimposed complex Fourier coefficients of the damping aerodynamic force at the specified ND, and calculates the aerodynamic damping based on the work done by the damping aerodynamic force within one vibration cycle.

[0058] See attached document Figure 5 Step S100 involves identifying the range of components in the overall machine environment that affect aerodynamic damping calculations. This is performed through the component identification module and includes the following sub-steps.

[0059] Sub-step S101: Determine the target blade row for forced vibration aerodynamic damping analysis.

[0060] In this sub-step, the overall layout data of the target blade row in the turbomachinery to be analyzed is obtained. The overall layout data includes the axial position of the blade rows, the circumferential number of blade rows, the relative positions of the rotor and stator, the casing boundary position, the hub boundary position, and the flow direction. Based on the vibration safety analysis object, the target blade row for which forced vibration aerodynamic damping needs to be calculated is determined.

[0061] The target blade row is the blade row that exhibits a forced vibration response. The target blade row can be either a rotor blade row or a stator blade row. When determining the target blade row, record the total number of blades, the target vibration mode, the target vibration frequency, and the target operating conditions. The target operating conditions include the total inlet pressure, total inlet temperature, static outlet pressure, rotational speed, mass flow rate, and fluid properties.

[0062] Once the target blade row is determined, its upstream and downstream regions are used as the subsequent component selection targets. When the rotor blade row is the target blade row, the inlet guide vane, upstream stator blade row, downstream stator blade row, support plate, and measuring probe are all considered for evaluation. When the stator blade row is the target blade row, the upstream rotor blade row, downstream rotor blade row, support plate, and measuring probe are all considered for evaluation.

[0063] Sub-step S102: Analyze the influence of the upstream and downstream structures of the target blade row on unsteady disturbances.

[0064] In this sub-step, information about the blade rows and fixed structures before and after the target blade row is read along the airflow direction. For each structure to be evaluated, its axial spacing, circumferential repetition count, relative rotational speed, and boundary connection method with the target blade row are determined. Boundary connection methods include sliding plane connection, periodic boundary connection, and fixed wall boundary connection.

[0065] The system performs conduction and cutoff discrimination on unsteady pressure disturbances caused by the vibration of the target blade row. A conduction state indicates that the unsteady pressure disturbance can propagate within the flow channel and reach adjacent structures; a cutoff state indicates that the unsteady pressure disturbance cannot reach adjacent structures in the form of a propagating wave. The conduction and cutoff discrimination uses the target vibration frequency data, the circumferential modal characteristics of the blade row, local sound velocity, flow velocity, and channel geometry as inputs.

[0066] When the structure to be judged is within the conduction path of an unsteady pressure disturbance, or when the structure to be judged constitutes a reflection boundary, scattering boundary, or interaction boundary near the target blade row, the structure to be judged is retained in the computational domain. When the structure to be judged does not cause propagation, reflection, scattering, or coupling effects on the vibration-induced pressure disturbance of the target blade row, the structure to be judged is not included in the target CFD computational domain.

[0067] Sub-step S103 generates a list of components required for the overall machine environmental aerodynamic damping analysis.

[0068] In this sub-step, the structure retained in sub-step S102 is organized into a component list. The component list includes at least the target blade row, the upstream affected components of the target blade row, the downstream affected components of the target blade row, the casing boundary, and the hub boundary. For the case where the rotor and stator are arranged adjacently, the component list also includes the rotor-stator junction location.

[0069] The parts list is used to define the geometric extent of the subsequent CFD computation domain. Each part in the parts list has a corresponding geometry file, number of blades, number of channels, motion attributes, and boundary attributes. Motion attributes include stationary attributes and rotational attributes. Boundary attributes include inlet boundary, outlet boundary, periodic boundary, wall boundary, and slip plane boundary.

[0070] The data output by this sub-step includes the target blade row identifier, reference coordinate direction, target vibration frequency data, range of components to be modeled, rotor-stator boundary location, and boundary type. This output data is input into step S200 to construct the first and second calculation models.

[0071] See attached document Figure 6 Step S200 involves establishing two types of aerodynamic calculation models, including components affecting the entire machine. This is executed through the model building module and includes the following sub-steps.

[0072] Sub-step S201: Establish the overall machine environment fluid calculation domain and the boundary between the rotating and stationary phases.

[0073] In this sub-step, a fluid calculation domain is established based on the component list output in step S100. The fluid calculation domain includes the target blade discharge channel, the upstream channel of the target blade discharge, the downstream channel of the target blade discharge, the casing wall, the hub wall, and the channels of adjacent components.

[0074] For cases where different speed ranges are adjacent, a slip plane is set between the rotor and stator computational domains. The slip plane is used to transfer unsteady flow field information between adjacent computational domains. The flow rate, pressure, and velocity distributions on both sides of the slip plane are exchanged according to the interface interpolation rules of the CFD solver. The axial position of the slip plane coincides with the rotor-stator interface of the actual overall machine structure.

[0075] The computational domain mesh comprises the blade surface boundary layer mesh, the channel interior volume mesh, and the transition mesh near the stator-transition interface. The blade surface boundary layer mesh is used to analyze the pressure and shear stress distributions on the blade surface. The channel interior volume mesh is used to analyze the mainstream flow field. The transition mesh near the stator-transition interface is used to reduce unsteady load errors introduced by slip plane interpolation.

[0076] Sub-step S202: Establish the first calculation model in which all blades are stationary.

[0077] In this sub-step, a first computational model is established based on the fluid computational domain obtained in sub-step S201. In the first computational model, no vibration displacement is applied to any of the blades in the target blade row. The first computational model preserves the relative motion relationship between the rotor and stator, the inlet flow conditions, the outlet flow conditions, and the periodic boundary conditions in the overall machine environment.

[0078] The first computational model is used to obtain the aerodynamic excitation force caused by the upstream blade row, downstream blade row, support plate, measuring probe, or other obstacle structures in the whole machine environment. This aerodynamic excitation force has the same frequency component as the subsequent damping aerodynamic force at the target vibration frequency, so it cannot be separated from the damping aerodynamic force by frequency screening alone.

[0079] The output of the first computational model includes the surface pressure distribution of each blade, the time history of the blade's integral aerodynamic force, and the complex Fourier coefficients of the aerodynamic force at the target vibration frequency. The input step for the output of the first computational model is S300.

[0080] Sub-step S203: Establish a second calculation model that only references the blade vibration.

[0081] In this sub-step, a second computational model is established based on the same fluid computational domain obtained in sub-step S201. In the second computational model, a given vibration mode and a given vibration mode coordinate amplitude are applied only to the reference blade; the remaining blades in the target blade row are not subject to vibration displacement. The reference blade is the blade in the target blade row used to extract the influence coefficients.

[0082] In the second computational model, vibration displacements are applied to the reference blade surface through a dynamic mesh or equivalent harmonic boundary conditions. The given vibration modes are derived from structural modal analysis, and the given vibration frequencies are consistent with the target forced vibration frequencies. For the frequency domain harmonic method, the reference blade is located in the center of the multi-channel computational domain.

[0083] The output of the second computational model is the combined aerodynamic force resulting from the superposition of the aerodynamic excitation force and the damping aerodynamic force induced by blade vibration. The second computational model is identical to the first computational model except for the reference blade vibration boundary conditions; all other fluid boundary conditions, computational domain range, mesh topology, time step, and harmonic frequency settings are the same.

[0084] Sub-step S204: Select either the time-domain full-cycle calculation method or the frequency-domain harmonic method.

[0085] In this sub-step, a computational strategy is selected based on the target blade row size, computational resources, and required output format. When using the time-domain full-cycle computation method, a full-cycle model of the target blade row is established and three-dimensional unsteady CFD calculations are performed, directly recording the aerodynamic time history of each blade. When using the frequency-domain harmonic method, a multi-channel model is used for the target blade row, while single-channel or multi-channel models are used for the upstream and downstream structures affecting aerodynamic damping.

[0086] The time step of the full-cycle time-domain calculation method is set according to the target vibration period. The number of data sampling points within one vibration period is no less than the number of sampling points required to satisfy the Fourier transform. The harmonic order of the frequency-domain harmonic method includes at least the harmonic order corresponding to the target vibration frequency. Both calculation strategies output aerodynamic information at the target vibration frequency.

[0087] This sub-step also sets inlet boundaries, outlet boundaries, and periodic boundaries. The inlet boundary is used to specify the total inlet pressure, total inlet temperature, flow angle, or mass flow rate. The outlet boundary is used to specify the outlet static pressure or radial equilibrium condition. The periodic boundary is used to constrain the periodic correspondence between circumferential channels.

[0088] See attached document Figure 7 Step S300 involves separating the excitation force and damping force using the output results from two types of calculation models. This is performed through the force term separation module and includes the following sub-steps.

[0089] Sub-step S301: Obtain the aerodynamic excitation force results for all blades in a stationary state.

[0090] In this sub-step, unsteady CFD calculations are performed on the first computational model. After the calculation reaches periodic stability, the aerodynamic time history of each blade in the target blade row is recorded. The aerodynamic forces are obtained by integrating the pressure on the blade surface, and the direction of integration is consistent with the direction of the generalized force corresponding to the target vibration mode.

[0091] For the time-domain full-cycle calculation method, the recorded aerodynamic time history covers at least one target vibration cycle. For the frequency-domain harmonic method, the complex Fourier coefficients at the target vibration frequency are directly extracted. The results obtained from the first calculation model represent the aerodynamic excitation forces under the overall machine environment, excluding the damping aerodynamic forces caused by the vibration of the reference blade.

[0092] The results of the first calculation model are stored according to blade number. Each blade number corresponds to an aerodynamic time history or complex Fourier coefficients at a target vibration frequency. This data is used to perform subtraction with the output of the second calculation model for blades with the same blade number.

[0093] Sub-step S302: Obtain the synthetic aerodynamic results under the vibration state of the reference blade.

[0094] In this sub-step, unsteady CFD calculations are performed on the second computational model. In the second computational model, only the blades are referenced by a given vibration mode and the given vibration mode coordinate amplitude; the remaining blades remain in a non-vibrating state. After the calculation reaches periodic stability, the composite aerodynamic results for each blade in the target blade row are recorded.

[0095] The composite aerodynamic force output by the second computational model consists of two parts. One part is the aerodynamic excitation force in the overall machine environment, and the other part is the damping aerodynamic force caused by the vibration of the reference blade. The two parts have the same frequency at the target vibration frequency, so they need to be separated by subtracting the result from the first computational model.

[0096] The sampling time, sampling frequency, integration direction, and blade numbering rules of the second calculation model are consistent with those of the first calculation model. For the frequency domain harmonic method, the complex Fourier coefficients output by the second calculation model correspond to the same target vibration frequency. This setting is used to ensure consistency of the phase reference in the difference processing.

[0097] Sub-step S303 calculates the damping aerodynamic force of each blade based on the linear superposition relationship.

[0098] In this sub-step, under small amplitude vibration conditions, the second calculation model will be... The combined aerodynamic force of each blade is represented as the superposition of the aerodynamic excitation force and the vibration-induced damping aerodynamic force of the same blade in the first calculation model. The time history of the damping aerodynamic force of each blade is obtained by subtracting the results under the same blade number.

[0099] The formula for calculating the time history of damped aerodynamic forces is as follows:

[0100] ;

[0101] in, For the first The time history of damping aerodynamic force of a blade, in N, represents the load of damping aerodynamic force induced by blade vibration as a function of time. For reference, in the blade vibration model, the first... The time history of the composite aerodynamic force of a blade, in N, represents the load of the aerodynamic force as a function of time after the superposition of aerodynamic excitation force and damping aerodynamic force. For all blade static models, the first The time history of the aerodynamic excitation force of the first blade, expressed in N, represents the effect of the unsteady flow field of the overall machine environment on the first blade. Excitation load on each blade; The blade number represents the blade position number in the target blade row, and is an integer. The unit is time, expressed in seconds (s), representing an instantaneous moment in the blade's vibration process.

[0102] The above calculations are performed on each blade in the target blade row that participates in the identification of influence coefficients. Through this difference processing, aerodynamic excitation and damping aerodynamic forces are separated under the condition that the target vibration frequency is the same. This processing does not rely on screening different frequency components in the spectrum.

[0103] Sub-step S304 obtains the complex Fourier coefficients of the damping aerodynamic force at the target vibration frequency.

[0104] In this sub-step, a Fourier transform is performed on the time history of the damping aerodynamic force to obtain the complex Fourier coefficients of the damping aerodynamic force at the target vibration frequency. These complex Fourier coefficients contain the amplitude and phase of the damping aerodynamic force at the target vibration frequency and are used for subsequent superposition of influence coefficients.

[0105] The formula for calculating the complex Fourier coefficients of damping aerodynamic forces is as follows:

[0106] ;

[0107] in, For the first The complex Fourier coefficient of the damping aerodynamic force of each blade at the target vibration frequency, in N, represents the amplitude and phase of the blade vibration-induced damping force at the target vibration frequency. The blade vibration period, measured in seconds, represents the time it takes for the blade to complete one forced vibration. The imaginary unit represents the condition that... plural units; The angular frequency of the blade vibration is expressed in rad / s, representing the angular frequency of the forced vibration of the blade.

[0108] For the frequency domain harmonic method, both the first and second calculation models directly output the complex Fourier coefficients at the target vibration frequency. Therefore, the complex Fourier coefficients of the damping aerodynamic force are obtained using complex difference. The complex difference calculation formula is as follows:

[0109] ;

[0110] in, For the first The complex Fourier coefficient of the damping aerodynamic force of each blade at the target vibration frequency, in N, represents the amplitude and phase of the blade vibration-induced damping force at the target vibration frequency. For reference, in the blade vibration model, the first... The complex Fourier coefficients of the composite aerodynamic force of each blade at the target vibration frequency, in N, represent the amplitude and phase of the composite aerodynamic force at the target vibration frequency. For all blade static models, the first The complex Fourier coefficients of the aerodynamic excitation force of each blade at the target vibration frequency, in units of N, represent the amplitude and phase of the aerodynamic excitation force at the target vibration frequency.

[0111] See attached document Figure 8 Step S400 involves calculating the aerodynamic damping for different section diameters based on the superposition of influence coefficients. This is performed through the damping calculation module and includes the following sub-steps.

[0112] Sub-step S401: Determine the phase angle between blades based on the section diameter and the total number of blades.

[0113] In this sub-step, the total number of blades in the target blade row and the specified section diameter are read. The total number of blades is determined by the geometric arrangement of the target blade row. Specify the nodal diameter. The results are given by forced vibration response analysis or detuned response analysis. Different Corresponding to different circumferential phase distributions.

[0114] Adjacent blades in the specified The formula for calculating the phase angle is as follows:

[0115] ;

[0116] in, The phase angle between blades, in rad, represents the phase angle between adjacent blades at a specified nodal diameter. Vibration phase difference under vibration modes; The nodal diameter number represents the nodal diameter number of the target blade row circumferential vibration mode, and is an integer. The total number of blades in the target blade row represents the number of blades arranged circumferentially in the target blade row, and is a positive integer.

[0117] For a given section diameter There is a fixed phase difference between adjacent blades in the target blade row. This phase difference is used to convert the damping aerodynamic influence coefficients corresponding to different blade numbers to the reference blade phase reference.

[0118] Sub-step S402 involves phase superposition of the damping aerodynamic influence coefficients for different blades.

[0119] In this sub-step, based on the influence coefficient method, the complex Fourier coefficients of the damping aerodynamic forces corresponding to different blades are determined according to the specified nodal diameter. Phase superposition is performed. Each blade number corresponds to a damping aerodynamic influence coefficient, which characterizes the contribution of that blade to the damping aerodynamic force of the reference blade when vibrating relative to the reference blade.

[0120] Specify The formula for calculating the complex Fourier coefficients of the damped aerodynamic forces after superposition is as follows:

[0121] ;

[0122] in, For specified The combined damping aerodynamic complex Fourier coefficients, in N, represent the specified... The amplitude and phase of the equivalent damping aerodynamic force acting on the reference blade under vibration mode; For the first The complex Fourier coefficient of the damping aerodynamic force of each blade at the target vibration frequency, in N, represents the amplitude and phase of the blade vibration-induced damping force at the target vibration frequency. The blade number represents the blade position number in the target blade row, and is an integer. This is the upper limit of the leaf number that participates in the superposition of influence coefficients. It represents the range of leaves participating in the linear superposition and is rounded to an integer. The imaginary unit represents the condition that... plural units; The phase angle between blades, measured in rad, represents the phase angle between adjacent blades at a specified distance. Vibration phase difference under vibration modes; The reference blade number represents the blade position number to which a given vibration mode and a given vibration mode coordinate amplitude are applied, and is an integer.

[0123] In frequency domain harmonic calculations, the range of blades involved in the superposition of influence coefficients is determined by the multi-channel computational domain of the target blade array. When the reference blade is located in the center of the computational domain, the influence coefficients on both sides of the reference blade are included in the superposition range. The result obtained after superposition is the specified... The equivalent damping aerodynamic complex Fourier coefficients corresponding to the lower reference blade.

[0124] Sub-step S403 calculates the work done by the damping aerodynamic force during one vibration cycle.

[0125] In this sub-step, according to the specified The superimposed complex Fourier coefficients of the damping aerodynamic forces are used to construct the time history of the damping aerodynamic forces at the target vibration frequency. Based on the blade's angular frequency and the given vibration mode coordinate amplitude, the vibration displacement and vibration velocity time histories of the reference blade are constructed. This damping aerodynamic force time history is multiplied by the reference blade's vibration velocity time history and integrated over one vibration cycle to obtain the work done by the damping aerodynamic forces on the reference blade's vibration.

[0126] Specify The formula for calculating the time history of lower damped aerodynamic forces is as follows:

[0127] ;

[0128] in, For specified The time history of the damped aerodynamic forces after superposition is expressed in N, representing the specified time history. The equivalent damping aerodynamic force acting on the reference blade under vibration mode is a time-varying load. For operations involving the real part, it represents the real part of the actual time history in the complex form of the load; For specified The combined damping aerodynamic complex Fourier coefficients, in N, represent the specified... The amplitude and phase of the equivalent damping aerodynamic force acting on the reference blade under vibration mode; The imaginary unit represents the condition that... plural units; The angular frequency of the blade vibration is expressed in rad / s, representing the angular frequency of the forced vibration of the blade. The unit is time, expressed in seconds (s), representing an instantaneous moment in the blade's vibration process.

[0129] The formula for calculating the time history of blade vibration displacement is as follows:

[0130] ;

[0131] in, The vibration displacement time history of the reference blade is expressed in meters (m), representing the instantaneous displacement of the reference blade along a given mode direction. The amplitude of the given vibration mode coordinates of the reference blade is expressed in meters (m), representing the amplitude of the vibration displacement of the reference blade along the given mode direction. The angular frequency of the blade vibration is expressed in rad / s, representing the angular frequency of the forced vibration of the blade. The unit is time, expressed in seconds (s), representing an instantaneous moment in the blade's vibration process.

[0132] The time history of the reference blade vibration velocity is obtained by differentiating the time history of the reference blade vibration displacement with respect to time. The calculation formula is as follows:

[0133] ;

[0134] in, The time history of the vibration velocity of the reference blade is expressed in m / s, representing the instantaneous velocity of the reference blade along a given mode direction. The amplitude of the given vibration mode coordinates of the reference blade is expressed in meters (m), representing the amplitude of the vibration displacement of the reference blade along the given mode direction. The angular frequency of the blade vibration is expressed in rad / s, representing the angular frequency of the forced vibration of the blade. The unit is time, expressed in seconds (s), representing an instantaneous moment in the blade's vibration process.

[0135] The formula for calculating the work done by the damping aerodynamic force during one vibration cycle is as follows:

[0136] ;

[0137] in, The work done by the damping aerodynamic force in one vibration cycle is measured in J, which represents the change in vibration energy caused by the interaction between the airflow and the blade vibration. For specified The time history of the damped aerodynamic forces after superposition is expressed in N, representing the specified time history. The equivalent damping aerodynamic force acting on the reference blade under vibration mode is a time-varying load. The time history of the vibration velocity of the reference blade is expressed in m / s, representing the instantaneous velocity of the reference blade along a given mode direction. The blade vibration period, measured in seconds, represents the time it takes for the blade to complete one forced vibration. The unit is time, expressed in seconds (s), representing an instantaneous moment in the blade's vibration process.

[0138] The sign of the aforementioned work value is determined by the phase relationship between the damping aerodynamic force and the vibration velocity. When the calculated work value corresponds to energy dissipation, it is used as the input for aerodynamic damping calculation. In engineering implementation, a sign convention can be used to treat the dissipated work value as a positive value before inputting it into the aerodynamic damping calculation.

[0139] Sub-step S404: Calculate the aerodynamic damping at a specified section diameter based on the periodic work and vibration amplitude.

[0140] In this sub-step, the specified work done by the damping aerodynamic force within one vibration cycle, the blade's circular frequency, and the amplitude of the given vibration mode coordinates are calculated. The aerodynamic damping is then applied. This aerodynamic damping serves as the damping parameter for the target blade under the overall machine environment, and is used for subsequent blade amplitude prediction or vibration safety analysis.

[0141] The formula for calculating aerodynamic damping is as follows:

[0142] ;

[0143] in, is the aerodynamic damping ratio, which represents the equivalent damping capacity of the fluid action on the blade vibration; The work done by the damping aerodynamic force in one vibration cycle is measured in J, which represents the change in vibration energy caused by the interaction between the airflow and the blade vibration. Modal mass, in kg; The angular frequency of the blade vibration is expressed in rad / s, representing the angular frequency of the forced vibration of the blade. The amplitude of the given vibration mode coordinates of the reference blade is expressed in meters (m), representing the amplitude of the vibration displacement of the reference blade along the given mode direction.

[0144] For different By repeating sub-steps S401 to S404, different results can be obtained. The corresponding aerodynamic damping distribution. This aerodynamic damping distribution can be input into a mistuned response analysis model or a forced vibration response analysis model to calculate the vibration response of the target blade array under different circumferential phase distributions.

[0145] Specific application examples:

[0146] See attached document Figure 9 This figure uses the number of section diameters as the horizontal axis and aerodynamic damping as the vertical axis to show the aerodynamic damping distribution corresponding to different section diameters. Figure 9 The results include three prediction curves: the single-blade row model prediction curve, the whole-machine model prediction curve, and the full-model method result. The full-model method result involves calculating the diameter of each section separately and only displays the diameters of a few sections. Figure 9It can simultaneously characterize the impact of different modeling ranges on aerodynamic damping prediction results, and the process of obtaining multiple aerodynamic damping results through one-time influence coefficient extraction and multiple phase superposition.

[0147] In a specific application embodiment, the target blade row is rotor blade row 2 in a certain type of axial flow turbomachinery. The total number of blades in the target blade row is 28. After identification in step S100, the inlet guide vane 1, rotor blade row 2, and stator blade row 3 ( Figure 2 All are included in the CFD calculation domain of the whole machine environment. One blade from the target blade row is selected as the reference blade.

[0148] In this specific application embodiment, the target vibration frequency is 7850Hz, the blade vibration circular frequency is 49377rad / s, and the amplitude of the given vibration mode coordinates of the reference blade is 1.0×10⁻⁶. -4 m. A slip plane boundary is set at the junction of the rotor and stator. In the first calculation model, no vibration displacement is applied to any blades, while in the second calculation model, only the blades are subjected to given modal vibration and given vibration modal coordinate amplitudes.

[0149] After performing CFD calculations on the first computational model, the aerodynamic excitation forces of all blades in a static state are obtained. After performing CFD calculations on the second computational model, the combined aerodynamic force of the reference blade in a vibrating state is obtained. Subtracting the aerodynamic excitation forces of the same blade number in the first computational model from the combined aerodynamic forces of the same blade number in the second computational model yields the damping aerodynamic force corresponding to each blade number.

[0150] Substituting the damping aerodynamic force complex Fourier coefficients corresponding to each blade number, the inter-blade phase angle, the reference blade number, and the upper limit of the blade number participating in the superposition of influence coefficients into the calculation formula for the superimposed damping aerodynamic force complex Fourier coefficients under the specified ND, we obtain the superimposed damping aerodynamic force complex Fourier coefficients under the specified ND as follows: Figure 9 As shown in the figure. Based on this set of results, aerodynamic damping calculation curves are generated for different nodal diameters (ND). These curves are used to provide damping inputs for different circumferential phase distributions to the detuned response analysis model.

[0151] Based on the above parameter values, a comparison was made between the traditional three-dimensional unsteady CFD energy method (29 calculations, including 28 blade vibration calculations and 1 blade fixation calculation) and the method of this invention (2 calculations). The number of calculations was reduced from 29 to 2. Within the same section diameter range, the aerodynamic damping values ​​of the method of this invention and the traditional three-dimensional unsteady CFD energy method are highly consistent. Therefore, it is determined that, while retaining... Figure 2Under the influence of the overall machine environment, including the inlet guide vane 1, rotor blade row 2, and stator blade row 3, this invention can obtain the aerodynamic damping under different nodal diameters (ND) by superimposing two types of calculation models and influence coefficients, and use this aerodynamic damping as the input parameter for the forced vibration response analysis of the target blade row. Furthermore, compared to the traditional three-dimensional unsteady CFD energy method, this invention reduces the number of CFD calculations while maintaining consistency in the calculation results, thereby improving the engineering applicability of the aerodynamic damping assessment for forced vibration of blades under the overall machine environment.

Claims

1. A method for determining the aerodynamic damping of forced vibration of blades under whole-machine conditions, characterized in that, Includes the following steps: Acquire the overall layout data of the target blade row and the target vibration frequency data, identify the components that affect aerodynamic damping, and generate a component list; Based on the component list, a fluid computational domain is established, and a first computational model in which all blades are stationary and a second computational model in which only blade vibration is referenced are established. Unsteady aerodynamic forces are calculated on the first and second calculation models to obtain aerodynamic excitation forces and composite aerodynamic forces. The damping aerodynamic force is obtained by subtracting the combined aerodynamic force from the aerodynamic excitation force. The damping aerodynamic force influence coefficient is obtained based on the damping aerodynamic force. The damping aerodynamic force influence coefficient is then superimposed on the phase of the damping aerodynamic force influence coefficient based on the specified section diameter ND to obtain the superimposed complex Fourier coefficient of the damping aerodynamic force under the specified ND. The aerodynamic damping is then calculated based on the superimposed complex Fourier coefficient of the damping aerodynamic force under the specified ND.

2. The method for determining the aerodynamic damping of forced vibration of blades under whole-machine environment according to claim 1, characterized in that, The specific steps for identifying components that affect aerodynamic damping and generating a component list are as follows: Based on the overall machine layout data, determine the target blade row for forced vibration aerodynamic damping analysis; The blade rows and fixed structure information before and after the target blade row are read along the airflow direction, which are used as the upstream and downstream structures of the target blade row. Based on the target vibration frequency data, blade circumferential modal characteristics, local sound velocity, flow velocity, and channel geometry, determine the propagation, reflection, scattering, or coupling effects of the upstream and downstream structures on the unsteady pressure disturbance induced by blade vibration. Structures that have propagation, reflection, scattering, or coupling effects are identified as components that affect aerodynamic damping, and a list of these components is generated.

3. The method for determining the aerodynamic damping of forced vibration of blades under whole-machine environment according to claim 1, characterized in that, The specific steps for establishing the fluid computational domain based on the aforementioned component list are as follows: The component list shall include at least the target blade row, the upstream influencing component of the target blade row, the downstream influencing component of the target blade row, the casing boundary, and the hub boundary; For cases where different speed ranges are adjacent, a sliding plane is set between the rotor computational domain and the stator computational domain; In the fluid computation domain, inlet boundary, outlet boundary, periodic boundary, wall boundary, and sliding plane boundary are set.

4. The method for determining the aerodynamic damping of forced vibration of blades under whole-machine environment according to claim 1, characterized in that, The specific steps for establishing the first calculation model where all blades are stationary and the second calculation model that only references blade vibration are as follows: The first computational model and the second computational model are established based on the same fluid computational domain; In the first calculation model, all blades of the target blade row are not subjected to vibration displacement; In the second calculation model, only the reference blade is subjected to a given vibration mode and a given vibration mode coordinate amplitude, while the remaining blades in the target blade row are not subjected to vibration displacement.

5. The method for determining the aerodynamic damping of forced vibration of blades under whole-machine environment according to claim 1, characterized in that, The specific steps for performing unsteady aerodynamic calculations on the first and second calculation models are as follows: When using the time-domain full-cycle calculation method, a full-cycle model of the target blade is established and three-dimensional unsteady calculations are performed to output the aerodynamic time history of each blade. Alternatively, the frequency domain harmonic method can be used to calculate the harmonic order corresponding to the target vibration frequency, and the complex Fourier coefficients corresponding to each blade can be directly output at the specified harmonic frequency. The first calculation model and the second calculation model use the same fluid boundary conditions, the same fluid property parameters, the same mesh topology, and the same target vibration frequency.

6. The method for determining the aerodynamic damping of forced vibration of blades under whole-machine environment according to claim 1, characterized in that, The specific steps for obtaining the aerodynamic excitation force and the combined aerodynamic force are as follows: Unsteady aerodynamic force calculations are performed on the first calculation model, and the aerodynamic force results of each blade under the condition that all blades are stationary are recorded. The aerodynamic force results of each blade under the condition that all blades are stationary are used as the aerodynamic excitation force. Unsteady aerodynamic force calculations are performed on the second calculation model, and the aerodynamic force results of each blade under the reference blade vibration state are recorded. The aerodynamic force results of each blade under the reference blade vibration state are used as the composite aerodynamic force. The aerodynamic excitation force and the combined aerodynamic force have the same blade number, the same target vibration frequency, and the same data sampling interval.

7. The method for determining the aerodynamic damping of forced vibration of blades under whole-machine environment according to claim 1, characterized in that, The specific steps for obtaining the damping aerodynamic force by subtracting the combined aerodynamic force from the aerodynamic excitation force are as follows: Read the synthetic aerodynamic force of the corresponding blade in the second calculation model; Read the aerodynamic excitation force of the same blade in the first calculation model; Under the same blade number, the same target vibration frequency, and the same data sampling interval, the aerodynamic excitation force is subtracted from the synthetic aerodynamic force to obtain the damping aerodynamic force of the corresponding blade. Repeat the above process for each blade involved in the influence coefficient identification.

8. The method for determining the aerodynamic damping of forced vibration of blades under whole-machine environment according to claim 1, characterized in that, The specific steps for obtaining the damping aerodynamic influence coefficient based on the aforementioned damping aerodynamic force are as follows: When the unsteady aerodynamic force calculation adopts the time-domain full-cycle calculation method, the time history of the damping aerodynamic force of each blade is subjected to Fourier transform to obtain the complex Fourier coefficient of the damping aerodynamic force at the target vibration frequency. When the unsteady aerodynamic calculation uses the frequency domain harmonic method, the complex Fourier coefficients output by the first calculation model are directly subtracted from the complex Fourier coefficients output by the second calculation model. The obtained complex Fourier coefficients are used as the damping aerodynamic influence coefficients for each blade.

9. The method for determining the aerodynamic damping of forced vibration of blades under whole-machine environment according to claim 1, characterized in that, The specific steps for performing phase superposition of the damping aerodynamic influence coefficients based on the specified section diameter ND to obtain the superimposed complex Fourier coefficients of the damping aerodynamic forces under the specified ND are as follows: Read the total number of blades in the target blade row and the specified section diameter ND; The phase angle between adjacent blades in the specified ND vibration mode is determined based on the total number of blades and the specified section diameter ND. Using the reference blade as a phase reference, the damping aerodynamic influence coefficients corresponding to different blade numbers are converted to the reference blade phase reference. The damping aerodynamic influence coefficients converted to the reference blade phase reference are summed to obtain the superimposed complex Fourier coefficients of the damping aerodynamic forces under the specified ND.

10. The method for determining the aerodynamic damping of forced vibration of blades under whole-machine environment according to claim 1, characterized in that, The specific steps for calculating aerodynamic damping based on the superimposed complex Fourier coefficients of the damping aerodynamic forces under the specified ND are as follows: The damping aerodynamic time history can be constructed based on the superimposed complex Fourier coefficients of the damping aerodynamic forces under the specified ND, or the Fourier coefficients at the target vibration frequency can be used directly. Based on the blade vibration circular frequency and given vibration mode coordinate amplitude of the reference blade, construct the vibration displacement time history and vibration velocity time history of the reference blade, or construct the Fourier representation of the vibration displacement and vibration velocity of the reference blade. Multiply the damping aerodynamic force time history with the vibration velocity time history and integrate over one vibration cycle to obtain the work done by the damping aerodynamic force over one vibration cycle. The aerodynamic damping at the specified ND is calculated based on the work done by the damping aerodynamic force in one vibration cycle, the blade vibration circular frequency, and the amplitude of the given vibration mode coordinates.

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