CFD-beam unit time-frequency hybrid calculation method for predicting pipeline flow-induced vibration

Abstract

According to the CFD-beam unit time-frequency hybrid calculation method for predicting pipeline flow-induced vibration, a fluid load applying method acting on a beam unit is provided, a three-dimensional structure model is simplified into a one-dimensional beam unit, the calculation complexity is remarkably reduced on the premise that the precision is guaranteed, and efficient vibration prediction is achieved. The method comprises the following steps of: firstly, carrying out segmented discretization on regions with high turbulence intensity and pressure gradient dramatic change of a pipeline flow field, and calculating concentrated loads of each sub-region by utilizing boundary integration; and converting the time domain load into a frequency domain excitation source through Fourier transform, and finally enabling the excitation source to be equivalent to concentrated load vector input of a beam unit-based pipeline structure calculation model to realize efficient solving of frequency domain vibration response.

Description

Technical Field

[0001] The present invention relates to fluid-induced vibration of pipelines, and particularly to a CFD-beam element time-frequency hybrid calculation method for predicting fluid-induced vibration of pipelines. Background Art

[0002] Pipeline systems, as key carriers for transmitting fluid mass flow, energy flow, and momentum flow, are widely used in fields such as ocean engineering, shipbuilding industry, aerospace, etc. Under the action of internal fluid excitation and external environmental loads, pipeline systems will generate fluid pressure pulsation and wall structure vibration. The coupling of the two may trigger serious fluid-induced vibration phenomena. Such vibration will not only lead to fatigue damage of pipeline systems and their accessories, affecting the stability and safety of industrial systems such as automobiles, ships, and airplanes, but on the other hand, it will also generate noise radiation to the environment, forming noise pollution. The problem of vibration and noise is particularly prominent in ship pipeline systems. The vibration and noise of pipeline systems will generate sound radiation through the hull and internal and external fluid exchange, affecting the stealth performance of ships and directly posing a threat to safety. Therefore, in the initial design, scheme demonstration stage of pipeline systems and fault diagnosis and system re-optimization design after the pipeline is put into use, calculating, predicting, and analyzing its vibration and noise are important tasks for low-vibration design of pipeline systems.

[0003] The calculation methods of fluid-induced vibration mainly include time-domain-frequency-domain hybrid methods and full-time-domain methods. The time-domain-frequency-domain hybrid method can effectively predict the vibration characteristics caused by dynamic loads by using computational fluid dynamics (CFD) to obtain fluid excitation in the time domain and combining computational structural dynamics (CSD) to establish a structural model in the frequency domain. However, pipeline systems are typical chain structures, with characteristics such as large length-diameter ratio, numerous pipeline element forms, and complex spatial distribution, resulting in large computational amounts and low efficiency of this method. Although the full-time-domain method solves in the time domain in both the flow field and the structural field and can calculate the structural response without performing Fourier transform on the fluid excitation, it cannot directly use the frequency-domain data obtained from experiments as boundary conditions, resulting in poor adaptability and still difficult to meet the actual engineering requirements in terms of computational efficiency.

[0004] Currently, the CFD method based on high-precision turbulence models can accurately capture the pressure pulsation of the fluid inside the pipe and is widely used in the calculation of the flow field in fluid-structure interaction. The frequency-domain response analysis based on beam elements has significant advantages in solving pipeline vibration problems. It can simplify the geometric model while ensuring the calculation accuracy and shorten the calculation time. Beam elements mainly include Euler-Bernoulli beam elements and Timoshenko beam elements. Euler-Bernoulli beam elements assume that the cross-section of the beam remains perpendicular to the central axis before and after deformation and ignore axial strain, which is suitable for slender beams. Timoshenko beam elements consider shear deformation and moment of inertia on the basis of Euler-Bernoulli beam elements and are more suitable for short and thick beams. For pipeline systems, the characteristic of a large length-diameter ratio determines that Euler-Bernoulli beam elements are more suitable for them. Summary of the Invention

[0005] The present invention provides a CFD-beam element time-frequency hybrid calculation method for predicting fluid-induced vibration of pipelines, which combines the advantages of accurately calculating the pulsating pressure of the pipe wall by CFD and simplifying the structural model by Euler-Bernoulli beam elements, significantly improving the calculation efficiency while ensuring the calculation accuracy of fluid-induced vibration; and proposes an equivalent method of converting the time-domain distributed load of the fluid into a frequency-domain concentrated load to avoid the problems of computational resource dissipation and mapping time delay caused by data mapping at the grid element level.

[0006] A CFD-beam element time-frequency hybrid calculation method for predicting fluid-induced vibration of pipelines according to the present invention comprises the following steps:

[0007] Step 1: Based on the structure of the pipeline system to be measured, establish a fluid domain model and mesh the fluid domain;

[0008] Step 2: Establish a fluid mechanics control equation based on a high-precision turbulence model, and set boundary conditions, fluid parameters, and solution controls;

[0009] The control equation is:

[0010]

[0011] where u i represents the component of the velocity vector in the i direction; ρ f represents the fluid density; p represents the fluid pressure; δ ij represents the Kronecker symbol; μ represents the dynamic viscosity of the fluid; f i represents the component of the body force in the i direction.

[0012] Step 3: Extract the time-domain wall pulsating pressure in segments;

[0013] Obtain the in-pipe flow field information through CFD, identify the local complex regions with sharp changes in pressure gradient and high turbulence intensity, and discretize the pipeline axially according to the severity of the changes in both.

[0014] Step 4: Calculate the concentrated load in the time domain of the pipe segment using boundary integration;

[0015] For the straight pipe segment with steady flow, the frictional coupling caused by its internal flow viscosity and the pipe wall can be neglected. Finally, the concentrated load vector is obtained by boundary integration of the wall pressure distribution after segmentation and discretization.

[0016]

[0017] Among them, F i (t) represents the concentrated load vector varying with time for the i-th segment; A i represents the area vector of the i-th segment; p i (t) represents the fluid pressure of the i-th segment; dA represents the differential area vector.

[0018] Step 5: Obtain the concentrated load in the frequency domain of the pipe segment through Fourier transform;

[0019] The extracted concentrated load vector in the time domain is converted into a frequency-domain excitation source vector through Fourier transform. The concentrated load vector of the pipe wall fluid obtained by CFD calculation is a time-domain pulsating signal. Therefore, the calculated concentrated load vector in the time domain needs to be converted into a frequency-domain excitation source vector through the following formula as the load input for the beam element.

[0020]

[0021] Among them, F i (f) represents the concentrated load vector varying with frequency for the i-th segment; f represents the frequency; t represents the time; N is the time length;

[0022] Step 6: Based on the pipe segment division basis provided in Step 3, perform beam element pipe segment division;

[0023] Step 7: Add constraint conditions to the beam element. At this time, the concentrated load vector calculated in Step 5 is converted into a frequency-domain excitation source vector through Fourier transform as the load input for the beam element;

[0024] Select the Euler-Bernoulli beam element applicable to the long-diameter ratio pipeline system to establish a pipeline fluid-induced vibration calculation model. Considering that the interaction process between the internal flow of the pipeline and the pipeline is extremely complex, in order to simplify the analysis of the vibration characteristics based on the Euler-Bernoulli beam element, as Figure 2 shown, the following reasonable assumptions need to be introduced:

[0025] Assume that the fluid conveying pipeline is a circular pipe with a constant cross-section, pure elasticity, homogeneity, and isotropy, and the forces and displacements of the pipeline deformation satisfy the linear relationship described by Hooke's law.

[0026] Ignore the interaction between the pipe body and the fluid when the liquid-filled pipeline moves radially and rotates around the pipe axis;

[0027] Ignore the friction coupling effect between the pipe body and the fluid;

[0028] Assume that the fluid in the pipe is a single-phase fluid and there is no cavitation phenomenon;

[0029] Assume that the pressure and flow velocity of the fluid remain constant within the same cross-section of the pipeline and are stable during the pipeline transmission process.

[0030] Based on the above assumptions, the calculation equation for the fluid-induced vibration of the liquid-filled pipeline based on the Euler-Bernoulli beam element can be obtained:

[0031]

[0032] In the formula, M is the pipe body mass matrix; M f is the fluid mass matrix; C is the system damping matrix; K is the system stiffness matrix; F(t) is the time-domain fluid load; U(t) is the time-domain displacement.

[0033] The method for simplifying the analysis of the vibration characteristics by the Euler-Bernoulli beam element in step 7 is as follows: The Euler-Bernoulli beam element equivalently simulates the three-dimensional pipeline structure through a one-dimensional beam element, applies the boundary conditions of the fluid load based on the static equivalence principle, and forms a time-domain-frequency-domain unidirectional coupling method for the CFD-beam element. This method is based on structural mechanics, simplifies complex geometric features through one-dimensional modeling, and uses the static equivalence principle for fluid excitation transfer to achieve multi-physics coupling calculation in vibration response analysis.

[0034] Step 8: Calculate the pipeline vibration response;

[0035] Based on step 7, through Fourier transform, the following frequency-domain motion equation can be obtained:

[0036] [-(2πf) 2 (M + M f ) + j2πfC + K]U(f) = F(f)

[0037] where U(f) is the displacement to be solved in the frequency domain; F(f) is the excitation source in the frequency domain.

[0038] Step 9: Output the frequency-domain vibration response;

[0039] Combined with Saint-Venant's principle, the excitation source vector obtained by CFD is introduced into the flow-induced vibration calculation model, and the vibration response of the pipeline at the position to be investigated is obtained by combining with the finite element method.

[0040] For steps 1-9 of the CFD-beam element time-frequency hybrid calculation method for predicting pipeline flow-induced vibration described above, a method for applying fluid loads to beam elements is proposed: First, by segmenting and discretizing the regions with high turbulence intensity and sharp pressure gradient changes in the pipeline flow field, the time-domain concentrated loads of each sub-region are calculated using boundary integration; then, the time-domain loads are converted into frequency-domain excitation sources through Fourier transform, and finally, this excitation source is input as the concentrated load vector of the pipeline structure calculation model based on beam elements to achieve efficient solution of the frequency-domain vibration response.

[0041] The CFD-beam element time-frequency hybrid calculation method for predicting pipeline flow-induced vibration of the present invention has the following remarkable advantages:

[0042] 1. Taking the concentrated load as the input, there is no need to map the CFD node information to the finite element model, thus shortening the fluid excitation load application time, reducing the consumption of computing resources, and significantly improving the solution efficiency.

[0043] 2. Simplifying the three-dimensional structure model into one-dimensional beam elements, combined with the fluid load application method of equivalent distributed loads on the pipe wall into concentrated loads, obtaining the fluid excitation force in the frequency domain through Fourier transform, and using it as the load input at the nodes of the one-dimensional beam elements, finally realizing the three-dimensional CFD-beam element time-frequency domain hybrid solution, significantly reducing the computational complexity while ensuring the accuracy, and achieving efficient vibration prediction. Description of the Drawings

[0044] Figure 1 Is the calculation flow chart of the method of the present invention

[0045] Figure 2 Is the pipeline element model

[0046] Figure 3 Is the pipeline system

[0047] Figure 4 Is the radial excitation load (taking eight segments as an example)

[0048] Figure 5 Is the equivalent load application position

[0049] Figure 6 Is the numerical calculation verification at point A (different number of segments)

[0050] Figure 7 Is the numerical calculation verification at point B (different number of segments)

[0051] Figure 8 Is the numerical calculation verification at point A (different forms of load application ranges)

[0052] Figure 9 Numerical calculation verification for point B (different forms of load application range)

[0053] Figure 10 Numerical calculation verification for point A (different forms of load input)

[0054] Figure 11 Numerical calculation verification for point B (different forms of load input)

[0055] Figure 12 Experimental verification for point A

[0056] Figure 13 Experimental verification for point B Specific implementation manners

[0057] The following specifically describes a CFD-beam element time-frequency hybrid calculation method for predicting pipeline flow-induced vibration according to the present invention in combination with specific examples:

[0058] Embodiment

[0059] Taking a 90° elbow and an extended straight pipe as the research object, as Figure 3 shown.

[0060] (1) In terms of numerical calculation verification:

[0061] Focus on the local coupling effect caused by connection coupling and Bourdon coupling in the 90° elbow. The CFD calculation based on a high-precision turbulence model shows that the turbulent kinetic energy and pressure distribution in the elbow region are significantly non-uniform - high pressure gradients and strong turbulence regions are concentrated in the elbow part, and the flow field deformation in this part is the main inducement of the coupling effect.

[0062] The embodiment of the present invention adopts a CFD-beam element time-frequency hybrid calculation method for predicting pipeline flow-induced vibration, and the steps are as follows:

[0063] Step 1: Based on the structure of the pipeline system to be measured, establish a fluid domain model and perform mesh division on the fluid domain;

[0064] Step 2: Establish a fluid mechanics control equation based on a high-precision turbulence model, and set boundary conditions, fluid parameters and solution controls;

[0065] Step 3: Extract the time-domain wall pulsating pressure in segments; obtain the flow field information in the pipe through CFD, identify local complex regions with sharp changes in pressure gradient and high turbulence intensity, and discretize the pipeline along the axial direction according to the severity of the changes. The embodiment of the present invention discretizes the elbow region into two / four / eight / sixteen segments using different segmentation scales;

[0066] Step 4: Calculate the time-domain concentrated load of the pipe segment using boundary integration;

[0067] Step 5: Obtain the frequency-domain concentrated load of the pipe segment through Fourier transform;

[0068] The extracted time-domain concentrated load vector is converted into a frequency-domain excitation source vector through Fourier transform. The wall-fluid concentrated load vector obtained from CFD calculation is a time-domain pulsating signal. Therefore, the calculated time-domain concentrated load vector needs to be converted into a frequency-domain excitation source vector through the following formula as the load input for the beam element.

[0069]

[0070] where, F i (f) represents the concentrated load vector of the i-th segment varying with frequency; f represents frequency; t represents time; N is the time length;

[0071] The magnitude of the excitation source is as Figure 4 shown, considering the load input in the form of complex numbers / amplitude.

[0072] Step 6: Perform beam element pipe segment division based on the pipe segment division criteria provided in Step 3;

[0073] Step 7: Add constraint conditions to the beam element. At this time, the calculated time-domain concentrated load vector is converted into a frequency-domain excitation source vector through Fourier transform in Step 5 as the load input for the beam element;

[0074] Construct a one-dimensional pipeline model based on Euler-Bernoulli beam elements, and apply the concentrated load vector to the corresponding nodes of the one-dimensional pipeline model, as Figure 5 shown.

[0075] Step 8: Calculate the pipeline vibration response;

[0076] Based on Step 7, through Fourier transform, the following frequency-domain motion equation can be obtained:

[0077] [-(2πf) 2 (M + M f ) + j2πfC + K]U(f) = F(f)

[0078] where, U(f) is the displacement to be solved in the frequency domain; F(f) is the frequency-domain excitation source.

[0079] Step 9: Output the frequency-domain vibration response;

[0080] Combined with Saint-Venant's principle, the excitation source vector obtained from CFD is brought into the fluid-induced vibration calculation model, and the vibration response of the pipeline at the position to be investigated is obtained by combining the finite element method.

[0081] The flange is equivalent to a concentrated mass, and the fixed support is used as the boundary condition. Based on the FEM, the vertical / radial vibration responses at points A and B are obtained from the calculation model, and the results are as Figures 6 to 11 shown:

[0082] When the elbow region is discretized into two / four segments, the radial vibration response is basically in agreement with the calculation results of the full-time domain method, but the vertical vibration level is significantly lower at 20 - 110 Hz, showing a large difference from the full-time domain method. When the elbow region is discretized into eight segments, its vertical / radial vibration calculation results are in good agreement with those obtained by the full-time domain method. This shows that the number of segments of fluid excitation has a significant impact on the calculation accuracy. The reason is that during the process of simplifying the distributed load to a concentrated load through boundary integration, there are deviations between the main vector of the obtained concentrated force and its main moment on the application position and the original distributed load, which leads to distortion of excitation transmission. As the number of segments increases (N≥8), the load application position gradually approaches the original load distribution position, and the vibration response results tend to be consistent.

[0083] Using a CFD-beam element time-frequency hybrid calculation method for predicting pipe flow-induced vibration, the loads at the elbow part, the loads in the regions 1, 2, 5, and 14 times the pipe diameter length upstream and downstream of the elbow part, and the loads in the entire region are calculated respectively, and the vibration response results are compared with these loads as the excitation sources: When the loads in the regions 2 times the pipe diameter length upstream and downstream of the elbow part are used as the excitation source, the vibration response results are in good agreement with those under the loads in the entire region. The reason is that the fluid flow in the straight pipe section is stable and the pulsating pressure intensity is low, and its influence on the pipe vibration response can be ignored, indicating that it is feasible to calculate the pipe flow-induced vibration characteristics with local loads (the regions 2 times the pipe diameter length upstream and downstream of the elbow part) as the excitation source.

[0084] Using a CFD-beam element time-frequency hybrid calculation method for predicting pipe flow-induced vibration, when the amplitude load is input, the radial vibration response of the pipe is in good agreement with the full-time domain method, but the vertical vibration level is significantly higher. The reason is that there is a problem of missing phase information in fluid excitation (especially sensitive to the vertical component). The input of complex loads effectively solves the problem of vertical vibration level deviation by retaining the complete frequency domain characteristics (including amplitude and phase information), verifying the necessity of the complex form in the analysis of elbow flow-induced vibration.

[0085] Conclusions verified by numerical calculations:

[0086] In the frequency band of 5 - 160 Hz, the flow-induced vibration responses calculated by the two methods are in good agreement, indicating that the method of calculating the pipe flow-induced vibration response in the present invention can achieve the same calculation accuracy as the full-time domain method. In addition, the calculation time of the method in the present invention is 45 s, and the full-time domain method takes 23 h 47 min. Comparing the calculation times of the two, it can be seen that using this method can significantly improve the calculation efficiency of pipe flow-induced vibration prediction on the premise of ensuring accuracy.

[0087] (2) In terms of experimental verification:

[0088] Steps 1-9 of a CFD-beam element time-frequency hybrid calculation method for predicting pipeline flow-induced vibration are used; a 90° elbow and an extended straight pipe are taken as the research objects; in step 3, the elbow area is discretized into eight segments, and concentrated loads in the upstream and downstream areas with a length of 2 times the pipe diameter are added; in step 7, a complex load input form is adopted, and a one-dimensional beam element is established based on the measured dynamic stiffness boundary conditions.

[0089] A calculation model of a 90° elbow and an extended straight pipe is established by using the full-time domain method; a fixed stiffness is used as the pipeline support boundary condition.

[0090] The vibration responses at points A and B are calculated by using the above two methods and compared with the test results. It can be seen from Figures 12 to 13 that: for the CFD-beam element time-frequency hybrid calculation method for predicting pipeline flow-induced vibration of the present invention, the trends and magnitudes of the vibration responses at the two measurement points are in good agreement with the test results. The radial vibration responses are basically the same below 100 Hz, and there are certain errors in the vertical vibration responses in the frequency band of 30-90 Hz. However, compared with the full-time domain method, the method of the present invention has achieved a significant improvement in the prediction accuracy of pipeline flow-induced vibration, which verifies its feasibility in engineering applications.

[0091] Conclusion in terms of experimental verification: The method of the present invention shows good accuracy in predicting pipeline flow-induced vibration, further indicating that the calculation accuracy of this method can meet the requirements of engineering applications.

Claims

1. A CFD-beam element time-frequency hybrid calculation method for predicting flow-induced vibration of pipelines, characterized in that The calculation method is as follows: Step 1: Based on the structure of the pipeline system to be measured, establish a fluid domain model and mesh the fluid domain; Step 2: Establish the fluid mechanics control equations based on a high-precision turbulence model, and set boundary conditions, fluid parameters, and solution controls; Step 3: Extract the time-domain wall pulsating pressure in segments; Step 4: Calculate the time-domain concentrated load of the pipe segment using boundary integration; Step 5: Obtain the frequency-domain concentrated load of the pipe segment through Fourier transform; Step 6: Based on the pipe segment division basis provided in Step 3, perform beam element pipe segment division; Step 7: Add constraint conditions to the beam element. At this time, the time-domain concentrated load vector calculated through Fourier transform in Step 5 is converted into a frequency-domain excitation source vector, which is used as the load input of the beam element; Step 8: Calculate the pipeline vibration response; Step 9: Output the frequency-domain vibration response.

2. The CFD-beam element time-frequency hybrid calculation method for predicting the flow-induced vibration of a pipeline according to claim 1, wherein The control equation in Step 2 is: where, u i represents the component of the velocity vector in the i direction; ρ f represents the fluid density; p represents the fluid pressure; δ ij represents the Kronecker symbol; μ represents the dynamic viscosity of the fluid; f i represents the component of the body force in the i direction.

3. The CFD-beam element time-frequency hybrid calculation method for predicting flow-induced vibration of pipelines according to claim 1, characterized in that In Step 3, the internal flow field information of the pipe is obtained through CFD, the regions with sharp changes in pressure gradient and high turbulence intensity are identified, and the pipeline is discretized axially according to the severity of the changes in both; 4. The CFD-beam element time-frequency hybrid calculation method for predicting the fluid-induced vibration of a pipeline according to claim 1, characterized in that In Step 4, for the straight pipe segment with steady flow, the frictional coupling caused by its internal flow viscosity and the pipe wall can be ignored. Finally, the concentrated load vector is obtained by boundary integration of the wall pressure distribution after segmentation and discretization; Among them, F i (t) represents the concentrated load vector varying with time in the i-th segment; A i represents the area vector of the i-th segment; p i (t) represents the fluid pressure in the i-th segment; dA represents the differential area vector.

5. The CFD-beam element time-frequency hybrid calculation method for predicting flow-induced vibration of pipelines according to claim 1, characterized in that, In Step 5, the time-domain concentrated load vector extracted is converted into a frequency-domain excitation source vector through Fourier transform. The concentrated load vector of the pipe wall fluid obtained by CFD calculation is a time-domain pulsating signal. Therefore, the calculated time-domain concentrated load vector needs to be converted into a frequency-domain excitation source vector through the following formula as the load input of the beam element; Among them, F i (f) represents the concentrated load vector varying with frequency in the i-th segment; f represents frequency; t represents time; N is the time length; 6. The CFD-beam element time-frequency hybrid calculation method for predicting flow-induced vibration of pipelines according to claim 1, wherein, In Step 7, select the Euler-Bernoulli beam element applicable to the pipeline system with a large length-to-diameter ratio to establish a calculation model for fluid-induced vibration of the pipeline; considering that the interaction process between the internal flow of the pipeline and the pipeline is extremely complex, in order to simplify the analysis of vibration characteristics based on the Euler-Bernoulli beam element, the following reasonable assumptions need to be introduced: Assume that the fluid-conveying pipeline is a circular pipe with a constant cross-section, pure elasticity, homogeneity, and isotropy, and the force and displacement of the pipeline deformation satisfy the linear relationship described by Hooke's law; Ignore the interaction between the pipe body and the fluid during the radial movement and rotation around the pipe axis of the liquid-filled pipeline; Ignore the frictional coupling effect between the pipe body and the fluid; Assume that the fluid in the pipe is a single-phase fluid without cavitation; Assume that the pressure and flow velocity of the fluid are constant within the same cross-section of the pipeline and stable during the pipeline transmission process; Based on the above assumptions, the calculation equation for fluid-induced vibration of the liquid-filled pipeline based on the Euler-Bernoulli beam element can be obtained: where M is the mass matrix of the pipe body; M f is the fluid mass matrix; C is the system damping matrix; K is the system stiffness matrix; F(t) is the fluid load in the time domain; U(t) is the displacement in the time domain; The method for simplifying the analysis of vibration characteristics by the Euler-Bernoulli beam element in step 7 is as follows: The Euler-Bernoulli beam element equivalently simulates the three-dimensional pipeline structure through a one-dimensional beam element, applies the boundary conditions of fluid loads based on the principle of static equivalence, and forms a CFD-beam element time-frequency hybrid calculation method. This method is based on structural mechanics, simplifies complex geometric features through one-dimensional modeling, and uses the principle of static equivalence for fluid excitation transfer to achieve multi-physics coupling calculation in vibration response analysis.

7. The CFD-beam element time-frequency hybrid calculation method for predicting flow-induced vibration of pipelines according to claim 1, wherein In step 8, based on step 7, through Fourier transform, the following frequency-domain motion equation can be obtained: [-(2πf) 2 (M + M f ) + j2πfC + K]U(f) = F(f) where U(f) is the displacement to be solved in the frequency domain; F(f) is the excitation source in the frequency domain.

8. The CFD-beam element time-frequency hybrid calculation method for predicting flow-induced vibration of pipelines according to claim 1, characterized in that, In step 9, combining the Saint-Venant principle, the excitation source vector obtained by CFD is brought into the fluid-induced vibration calculation model, and the vibration response of the position to be investigated on the pipeline is obtained by combining the finite element method.

9. The CFD-beam element time-frequency hybrid calculation method for predicting flow-induced vibration of pipelines according to claim 1, characterized in that When taking a 90° elbow and an extended straight pipe as the research object, in step 3, the elbow is discretized into eight segments, and concentrated loads are added to the upstream and downstream regions with a length of 2 times the pipe diameter; in step 7, a complex load input form is adopted, and a one-dimensional beam element is established based on the measured dynamic stiffness boundary conditions.

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