An aerodynamic damping analysis method based on influence coefficient method and vibration phase correction

Abstract

The application discloses a kind of aerodynamic damping analysis method based on influence coefficient method and vibration phase correction, it is related to the technical field of aerodynamic damping analysis of turbomachinery.The technical solution points include the following steps: according to the aerodynamic profile and structural model of blade, fluid domain model and solid domain model are established respectively;Carry out steady flow field analysis on fluid domain model, and provide initial field for non-steady flow field calculation;Modal analysis is carried out on solid domain model, and the natural frequency and modal shape of blade under rotating condition are obtained;Designate intermediate blade to vibrate according to the modal shape and natural frequency obtained, and carry out non-steady flow field analysis with steady flow field result as initial field;After calculation convergence, extract the aerodynamic force on blade surface, and calculate the aerodynamic work on blade under different pitch diameters.The application can give the situation under all pitch diameters by once non-steady flow field calculation, without multiple calculation of non-steady flow field under different pitch diameters, more quickly and efficiently, save calculation resources.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic damping analysis technology for turbomachinery, and more specifically, to an aerodynamic damping analysis method based on the influence coefficient method and vibration phase correction. Background Technology

[0002] Aeroelastic stability has been a subject of continuous research and attention from scholars. Currently, common numerical analysis methods for aeroelastic stability include the energy method, the eigenvalue method, and the time-domain method, with the energy method and the eigenvalue method being more commonly used in engineering.

[0003] The energy method analyzes aeroelastic stability from the perspective of work done. Given a blade vibrating according to a specific mode shape and frequency, it predicts flutter characteristics in that mode by calculating the energy exchange between the vibrating blade and the flow field. If the airflow does work on the blade, it indicates flutter; otherwise, it indicates no flutter. By expressing aerodynamic work as the modal aerodynamic damping ratio, it can be superimposed with mechanical damping, and the stability of the system can be judged based on the total damping. The energy method has clear physical meaning, fundamentally revealing the physical mechanism of flutter occurrence.

[0004] However, if the energy method is to be used to examine the aerodynamic damping under different nodal diameters, calculations need to be carried out separately for different nodal diameters. Although the model can be reduced by applying phase-shifting boundary conditions, which can significantly reduce the amount of calculation, it is still quite troublesome, and the more blades there are, the greater the amount of calculation. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide an aerodynamic damping analysis method based on the influence coefficient method and vibration phase correction. This method can provide the results for all nodal diameters with a single unsteady flow field calculation, eliminating the need for multiple calculations of unsteady flow fields for different nodal diameters. This method is faster, more efficient, and saves computational resources.

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

[0007] An aerodynamic damping analysis method based on the influence coefficient method and vibration phase correction, the method comprising the following steps:

[0008] S1. Establish fluid domain model and solid domain model respectively based on the aerodynamic shape and structural model of the blade;

[0009] S2. Perform steady flow field analysis on the fluid domain model and provide the initial field for unsteady flow field calculation;

[0010] S3. Perform modal analysis on the solid domain model to obtain the natural frequencies and mode shapes of the blade under rotation conditions;

[0011] S4. Specify the middle blade 0 to vibrate according to the obtained mode shape and natural frequency, and use the steady flow field results as the initial field to carry out unsteady flow field analysis;

[0012] S5. After convergence, extract the aerodynamic forces on the blade surface of the flow field and calculate the aerodynamic work W on the blade at a pitch diameter of k. k ;

[0013]

[0014] in,

[0015] This represents the aerodynamic force exerted on the surface of blade i by the vibration of blade 0 at time j under the k-th node diameter.

[0016] n tstep This represents the number of time steps within one oscillation cycle.

[0017] T represents the vibration period of the blade.

[0018] T i Here is the displacement transformation matrix.

[0019] This represents the vector composed of the displacement amplitudes of the nodal surfaces on blade number 0.

[0020] e is the base of the natural number.

[0021] ω is the natural frequency.

[0022] t j Let j be the time step.

[0023] Let be the phase difference between the displacement of blade i and the displacement of blade 0 at a diameter of k.

[0024] N is the number of blades in the entire ring.

[0025] Furthermore, the method further includes the following steps:

[0026] S6. Calculate the aerodynamic modal damping ratio ξ for different nodal diameters. k ;

[0027] Where u is the amplitude of the blade in the modal space.

[0028] Furthermore, in step S5, the aerodynamic work done by the unsteady aerodynamic force generated by the vibration of blade i on blade 0 is equal to the aerodynamic work done by the unsteady aerodynamic force generated by the vibration of blade 0 on blade -i.

[0029] In summary, the present invention has the following beneficial effects:

[0030] Using the method of this invention, the unsteady flow field can be calculated once to give the results for all nodal diameters, eliminating the need for multiple calculations of the unsteady flow field for different nodal diameters. This method is faster, more efficient, and saves computational resources. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the aerodynamic work performed on blade 0 in the embodiment.

[0032] Figure 2 This is a schematic diagram of the aerodynamic work done by blade 0 on the other blades in the embodiment. Detailed Implementation

[0033] The present invention will be further described in detail below with reference to the accompanying drawings.

[0034] This specific embodiment is merely an explanation of the present invention and is not intended to limit the invention. After reading this specification, those skilled in the art can make modifications to this embodiment without contributing any inventive step, but such modifications are protected by patent law as long as they are within the scope of the claims of the present invention.

[0035] Example:

[0036] An aerodynamic damping analysis method based on the influence coefficient method and vibration phase correction, the method comprising the following steps:

[0037] S1. Establish fluid domain model and solid domain model respectively based on the aerodynamic shape and structural model of the blade;

[0038] S2. Perform steady flow field analysis on the fluid domain model and provide the initial field for unsteady flow field calculation;

[0039] S3. Perform modal analysis on the solid domain model to obtain the natural frequencies and mode shapes of the blade under rotation conditions;

[0040] S4. Specify the middle blade 0 to vibrate according to the obtained mode shape and natural frequency, and use the steady flow field results as the initial field to carry out unsteady flow field analysis;

[0041] S5. After convergence, extract the aerodynamic forces on the blade surface of the flow field and calculate the aerodynamic work W on the blade at a pitch diameter of k. k ;

[0042] S6. Calculate the aerodynamic modal damping ratio ξ for different nodal diameters. k .

[0043]

[0044] in,

[0045] n represents the aerodynamic force exerted on the surface of blade i by the vibration of blade 0 at time j under the k-th node diameter. tstep The time step represents the number of vibration cycles, and T represents the vibration period of the blade. i Here is the displacement transformation matrix. This vector represents the amplitude of nodal displacements on the surface of blade 0, where e is the base of a natural number, ω is the natural frequency, and t... j Let j be the time step. Let N be the phase difference between the displacement of blade i and blade 0 at a diameter of k, and N be the number of blades in the entire ring.

[0046] In this embodiment, the vector is composed of the displacement amplitude of the surface node on blade 0. The quantity is known.

[0047] Where u is the amplitude of the blade in the modal space.

[0048] Of course, in addition to calculating the aerodynamic modal damping ratio under different pitch diameters, the aerodynamic work density distribution and the influence of adjacent blades can be further analyzed based on the aerodynamic work on the blades under different pitch diameters; that is to say, the method in this embodiment can not only provide system stability criteria, but also show more detailed information.

[0049] The following is the aerodynamic work W performed on the blade at the k-th node diameter in this embodiment. k The derivation and analysis process of the formula.

[0050] Aeroelastic instability in blades is caused by unsteady aerodynamic forces doing positive work on them. This typically manifests as the entire row of blades vibrating as a system at a common frequency. Therefore, the unsteady aerodynamic force generated by each blade will do positive or negative work on the other blades. Taking a specific blade (denoted as blade 0) as an example, refer to... Figure 1 The work done by unsteady aerodynamic forces on the blades is considered to be the sum of the work done by the unsteady aerodynamic forces caused by the vibration of each blade on blade 0.

[0051] That is, W = W 1，0 +W i，0 +…+W -i，0 +W -1，0 =∑W i，0 ;

[0052] in,

[0053] W i，0 This represents the work done by the unsteady aerodynamic force caused by the vibration of blade i on blade 0.

[0054] This represents the unsteady aerodynamic force generated at node m on the surface of blade 0 due to the vibration of blade i at time j. n represents the displacement of node m on the surface of blade 0 at time j. node This represents the total number of fluid nodes on the blade surface.

[0055] Reference Figure 2 The unsteady aerodynamic force caused by the vibration of blade 0 does work on other blades in the blade row; taking blade i as an example, the aerodynamic work W it receives from the vibration of blade 0 is... 0，i for:

[0056]

[0057] For the coordinated system, under the small perturbation assumption, the unsteady aerodynamic force on the surface of blade 0 caused by the vibration of blade i is equal to the aerodynamic force on the surface of blade -i caused by the vibration of blade 0.

[0058] That is, F i，0 =F 0，-i .

[0059] Therefore, the aerodynamic work done by the unsteady aerodynamic force caused by the vibration of blade i on blade 0 is equal to the aerodynamic work done by the unsteady aerodynamic force caused by the vibration of blade 0 on blade -i.

[0060] That is, W i，0 =W 0，-i .

[0061] Therefore, taking blade number 0 as an example, the aerodynamic work performed on the blade is:

[0062] W = W 0，1 +W 0，i +…+W 0，-i +W 0，-1 =∑W 0，i ;

[0063] Right now,

[0064] To determine the aerodynamic work on the blade, we only need to obtain the unsteady aerodynamic forces caused by the vibration of blade 0 on the surface of each blade and the displacement function of each blade.

[0065] In a coordinated system, when all blades vibrate synchronously, taking blade i as an example, its vibration displacement S i The displacement function of blade 0 can be obtained through the following transformation:

[0066]

[0067] in, T represents the vector composed of the displacement amplitudes of the nodal surfaces on blade 0. i This is the displacement transformation matrix;

[0068]

[0069] The change in nodal diameter causes a change in the phase of the displacement between blades. Therefore, the displacement S of blade i at nodal diameter k is... i，k for:

[0070]

[0071] in, The vector representing the displacement amplitudes of the nodal surfaces on blade i;

[0072] Let be the phase difference between the displacement of blade i and the displacement of blade 0 at a diameter of k.

[0073] The relationship with the pitch diameter k is as follows:

[0074]

[0075] Therefore, the aerodynamic work W on the blade at section k is... k for:

[0076]

[0077] The accuracy of the method in this embodiment can be verified using existing energy methods and eigenvalue methods. The method in this embodiment processes the blade displacement and performs a single unsteady flow field calculation to obtain results for any nodal diameter; compared to the energy method, it is faster, more efficient, and saves computational resources. Furthermore, based on the method in this embodiment, detailed information such as aerodynamic work density can be provided, and it can also be used to analyze the influence of adjacent blades on aerodynamic damping.

Claims

1. An aerodynamic damping analysis method based on the influence coefficient method and vibration phase correction, characterized in that, The method includes the following steps: S1. Establish fluid domain model and solid domain model respectively based on the aerodynamic shape and structural model of the blade; S2. Perform steady flow field analysis on the fluid domain model and provide the initial field for unsteady flow field calculation; S3. Perform modal analysis on the solid domain model to obtain the natural frequencies and mode shapes of the blade under rotation conditions; S4. Specify the middle blade 0 to vibrate according to the obtained mode shape and natural frequency, and use the steady flow field results as the initial field to carry out unsteady flow field analysis; S5. After convergence, extract the aerodynamic forces on the blade surface of the flow field and calculate the aerodynamic work W on the blade at a pitch diameter of k. k ; in, This represents the aerodynamic force exerted on the surface of blade i by the vibration of blade 0 at time j under the k-th node diameter. n step This represents the number of time steps within one oscillation cycle. T represents the vibration period of the blade. T i Here is the displacement transformation matrix. This represents the vector composed of the displacement amplitudes of the nodal surfaces on blade number 0. e is the base of the natural number. ω is the natural frequency. t j Let j be the time step. Let be the phase difference between the displacement of blade i and the displacement of blade 0 at a diameter of k. N is the number of blades in the entire ring.

2. The aerodynamic damping analysis method based on the influence coefficient method and vibration phase correction according to claim 1, characterized in that, The method further includes the following steps: S6. Calculate the aerodynamic modal damping ratio ξ for different nodal diameters. k ; Where u is the amplitude of the blade in the modal space.

3. The aerodynamic damping analysis method based on the influence coefficient method and vibration phase correction according to claim 1, characterized in that: In step S5, the aerodynamic work done by the unsteady aerodynamic force generated by the vibration of blade i on blade 0 is equal to the aerodynamic work done by the unsteady aerodynamic force generated by the vibration of blade 0 on blade -i.

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