A method for calculating the mode shape and harmonic response process of a pipeline in a booster area of a gas storage

Abstract

The present application belongs to the field of gas storage safety evaluation, and particularly relates to a kind of calculation method of mode shape and harmonic response process of gas storage pressurized zone pipeline.The present application includes: dividing grid and setting constraint for fluid domain and solid domain of pressurized zone pipeline three-dimensional model;Using prestressed coupled wet modal method to carry out fluid-solid coupling statics analysis to obtain initial prestress, and then calculate multi-order vibration wet modal;Based on the wet modal result, external excitation is applied, and direct complete harmonic response method is used to obtain deformation and stress concentration during vibration.The present application considers multi-load coupling, and fine modeling is carried out for dangerous positions such as welds and supports and high-pressure vessels.Adaptive meshing and high-precision constraint are used, and the calculation accuracy is greatly improved by innovatively combining prestressed wet modal and direct complete harmonic response analysis method, which provides strong support for pressurized zone pipeline design optimization, safety evaluation and maintenance, reduces safety risk and improves system reliability.

Description

Technical Field

[0001] This invention belongs to the field of gas storage safety assessment, and specifically relates to a method for calculating the vibration mode and harmonic response process of pipelines in the pressurization zone of a gas storage facility. Background Technology

[0002] Underground gas storage facilities are integrated underground and surface systems for natural gas injection, storage, and extraction. The pipeline system in the pressurization zone of the injection station is a crucial hub connecting the underground reservoir to the surface distribution network, undertaking the functions of injecting, storing, and extracting high-pressure natural gas. The pipelines in this pressurization zone operate under high pressure and variable operating conditions for extended periods, enduring the combined effects of prestressed supports, circumferential and axial stresses from high-pressure natural gas, vertical bending moments from the pipeline and fluid gravity, and dynamic excitations such as compressor vibration and fluid pulsation. This can easily induce resonance, leading to weld cracking, support loosening, and even pipeline rupture in the pressurization zone, threatening the security of the energy supply chain.

[0003] Current methods for assessing pipeline vibration in the pressurization zone of gas storage facilities have significant shortcomings: they employ a single-load calculation approach and simply superimpose the results. For example, although patent application CN115659721A combines beam and shell models and uses unidirectional fluid-structure interaction, it fails to establish a multi-load coupling framework, resulting in a large deviation from actual operating conditions. In reality, the coupling effects of support prestress, the "rigidification effect" of high pressure inside the pipe, and gravity bending moment fundamentally differ the dynamic characteristics of the pipeline in the pressurization zone from those under a single load, and traditional methods cannot capture this synergistic effect.

[0004] There are many simplifications and omissions in the modeling accuracy: the weld is simplified to a smooth transition structure, ignoring the local stress concentration caused by the weld reinforcement (most vibration fatigue failures originate from the weld toe); the support structure adopts the rigid constraint assumption and does not consider the stiffness nonlinearity of elastic supports such as rubber pads. For example, the patent application with publication number CN111881600A does not involve refined support modeling, resulting in excessive prestress transfer error; the connection between the high-pressure vessel and the pressurization zone pipeline is simplified to a rigid node, ignoring the influence of the vessel's self-weight on the stiffness matrix of the pressurization zone pipeline, which may overlook key resonance risks.

[0005] The accuracy of dynamic analysis is significantly flawed: modal analysis does not consider the influence of the initial stress field, and the use of stress-free state calculations leads to significant deviations in higher-order modal frequencies; harmonic response calculations often use the modal superposition method (ignoring the modal damping coupling effect) rather than the complete method. For example, the patent application with publication number CN115374559A is based on the equivalent analysis of the pipeline dynamic characteristics in the pressurization zone using fluid-structure interaction, but the calculation error of the resonance peak is often large, and it is impossible to accurately predict the location of maximum deformation and stress concentration.

[0006] These shortcomings lead to large errors in the vibration modal frequency of existing methods and deviations in stress response calculations during vibration exceeding 40%, which seriously restricts the safety assessment and optimization design of pipelines in pressurized areas. There is an urgent need for a high-precision calculation method that integrates detailed modeling, multi-load coupling, and accurate boundary conditions to support the safety management of pipelines throughout their entire life cycle in pressurized areas. Summary of the Invention

[0007] To address the aforementioned problems, in a first aspect, this invention proposes a method for calculating the mode shape and harmonic response process of a pipeline in the pressurization zone of a gas storage facility, comprising the following steps:

[0008] Mesh the fluid and solid domains of the 3D model of the pressurization zone pipeline, and set corresponding constraints on the structure in the 3D model of the pressurization zone pipeline.

[0009] The prestressed coupled wet modal method is used to perform fluid-structure coupled static analysis to obtain the initial prestress of the pipeline in the pressurization zone. Based on the initial prestress, the multi-order vibration wet modes of the pipeline in the pressurization zone are calculated using dynamic equations.

[0010] Based on the analysis results of multi-order vibration wet modes, an external excitation load matching the actual working conditions is applied, and dynamic analysis is performed using the direct complete harmonic response method to obtain the deformation distribution and stress concentration of the pipeline during vibration in the pressurization zone.

[0011] Furthermore, the three-dimensional model of the pressurization zone pipeline is a scaled model, including the geometric features and connection methods of welds, supports, and high-pressure vessels.

[0012] Furthermore, the fluid domain is divided using a tetrahedral mesh, with a boundary layer mesh set in the region near the pipe wall;

[0013] The solid domain is divided using a combination of hexahedral meshes as the primary method and tetrahedral meshes as the secondary method, with local mesh refinement at welds, supports, and high-pressure vessel connections.

[0014] Furthermore, the constraints include elastic constraints at the clamp supports, fixed or displacement constraints at the flanges, and elastic constraints on the walls and the ground.

[0015] Furthermore, the elastic constraint at the clamp support is determined according to the following steps:

[0016] Collect mechanical property data of the contact materials between the pipeline and the clamp in the pressurization zone, and establish a calculation model of the reaction force-deformation relationship between the clamp and the pipeline in the pressurization zone based on the mechanical property data;

[0017] Calculate the preload of a single bolt on the clamp based on the empirical formula for preload of carbon steel bolts;

[0018] Based on the pre-tightening force calculation results, the compressive stress distribution on the contact surface between the clamp and the pressurized pipeline is obtained through contact mechanics analysis, and the positive pressure under the initial compressive state is determined.

[0019] Based on the X, Y, and Z spatial coordinate axes, unidirectional stepwise displacement is applied to the pipeline in the pressurization zone under the initial compression state. The reaction force of the clamp on the pipeline in the pressurization zone is recorded, and the force-deformation curves in each direction are plotted.

[0020] The stiffness coefficients in the corresponding coordinate axis directions are calculated by the slope of the linear segment of the force-deformation curves in each direction, and these stiffness coefficients are used as elastic constraint conditions at the clamp support.

[0021] Furthermore, the type of constraint at the flange is determined based on the flange's connection relationship. If the flange is in contact with the ground, wall, or high-pressure vessel, a fixed constraint is applied; if the flange is suspended, a displacement constraint is applied.

[0022] Furthermore, the method of prestressed coupled wet modal analysis is used to perform fluid-structure coupled static analysis to obtain the initial prestress of the pipeline in the pressurization zone. Based on the initial prestress, the multi-order wet vibration modes of the pipeline in the pressurization zone are calculated using dynamic equations, including the following steps:

[0023] The static loads of the fluid and solids in the pressurization zone pipeline are applied, including the fluid pressure inside the pipe, the fluid gravity, the gravity of the pressurization zone pipeline, and the preload and frictional resistance of the bolts supporting the constraint.

[0024] Based on the applied static load, a fluid-structure interaction static analysis is performed to calculate the initial prestress of the pipeline in the pressurization zone under static load.

[0025] The initial prestress is mapped onto the three-dimensional model of the pipeline in the pressurization zone, and the multi-order wet vibration modes of the pipeline in the pressurization zone are calculated using dynamic equations.

[0026] Furthermore, the fluid pressure inside the pipe is determined based on the actual delivery pressure;

[0027] The fluid gravity is calculated based on the fluid density and the fluid volume in the pressurized zone pipe.

[0028] The gravity of the pressurization zone pipeline is calculated based on the density and volume of the pipeline material in the pressurization zone.

[0029] The preload of the bolt is calculated based on the yield strength of the bolt material and the cross-sectional area of ​​the bolt stress.

[0030] Furthermore, based on the analysis results of multi-order wet vibration modes, an external excitation load matching the actual working conditions is applied, and dynamic analysis is performed using the fully harmonic response method to obtain the deformation distribution and stress concentration of the pipeline during vibration in the pressurization zone, including the following steps:

[0031] Based on the natural frequency range in the multi-order vibration wet mode results, the frequency range and characteristics of the excitation load are determined, and an excitation load with corresponding characteristics is applied within this frequency range.

[0032] Based on the material and structural characteristics of the pressurized pipeline, determine the damping coefficient of the pressurized pipeline during normal operation that matches the excitation frequency range;

[0033] Based on the excitation load and vibration damping ratio, the dynamic equation is solved using the complete method, and the direct complete harmonic response is calculated to determine the deformation and stress distribution of the pressurized pipeline during vibration.

[0034] Extract the maximum deformation value of the pipeline in the pressurization zone and the stress concentration value in the dangerous area at the resonant frequency, analyze whether the maximum deformation value exceeds the safety limit and whether the stress exceeds the material fatigue limit, and confirm the resonance risk.

[0035] Furthermore, the excitation load satisfies the following formula:

[0036]

[0037] In the formula: F(t) is the instantaneous load amplitude at time t; F0 is the peak load value; Angular frequency, =2 f , f For frequency; This is the initial phase angle.

[0038] Secondly, this invention proposes a calculation system for the mode shape and harmonic response process of a pipeline in the pressurization zone of a gas storage facility, comprising:

[0039] The mesh generation and constraint setting module is used to mesh the fluid domain and solid domain of the 3D model of the pressurization zone pipeline, and to set corresponding constraints on the structure in the 3D model of the pressurization zone pipeline.

[0040] The fluid-structure interaction static and wet modal analysis module is used to perform fluid-structure interaction static analysis by coupling fluid loads and solid loads using the prestressed coupled wet modal method, to obtain the initial prestress of the pipeline in the pressurization zone, and to calculate the multi-order vibration wet modes of the pipeline in the pressurization zone using dynamic equations;

[0041] The Full Harmonic Response Analysis and Resonance Assessment Module is used to apply external excitation loads that match the actual working conditions, and to perform dynamic analysis using the direct full harmonic response method to obtain the deformation distribution and stress concentration of the pipeline during vibration in the pressurization zone.

[0042] Furthermore, the system also includes a 3D model building module for building a 3D model of the pressurization zone pipeline;

[0043] The three-dimensional model of the pressurization zone pipeline is a scaled model, including the geometric features and connection methods of welds, supports, and high-pressure vessels.

[0044] Thirdly, the present invention proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a method for calculating the mode shape and harmonic response process of the gas storage pressurization zone pipeline as described above.

[0045] Thirdly, the present invention proposes a computer program product, including a computer program / instruction, which, when executed by a processor, implements a method for calculating the mode shape and harmonic response process of the pipeline in the pressurization zone of the gas storage facility.

[0046] The beneficial effects of this invention are:

[0047] This invention takes into account the combined effects of prestress, internal pressure stress, pipeline gravity, and fluid gravity at different locations in the pressurization zone pipeline. At the same time, it fully considers dangerous locations such as welds and supports, as well as high-pressure vessels such as oil separators and washing tanks during the modeling process, making the calculation model closer to the actual situation and greatly improving the accuracy of the calculation results.

[0048] This invention, through the use of adaptive mesh generation technology and high-precision constraint settings, along with a rigorous calculation process, can reliably calculate the vibration modes and vibration response characteristics of pipelines in the pressurization zone. The calculation results can provide strong support for the design optimization, safety assessment, and maintenance of pipelines in the pressurization zone of gas storage and injection stations, effectively reducing the safety risks caused by pipeline vibration and improving the reliability of the transportation system.

[0049] This invention innovatively employs two methods: prestressed wet modal analysis and full harmonic response analysis. Prestressed wet modal analysis, by incorporating bolt preload and frictional resistance, as well as the gravity of the fluid inside the pipe, the gravity of the pressurized pipeline, and the initial stress field formed by the fluid gravity, and considering the coupling effect between the fluid inside the pipe and the pressurized pipeline, accurately captures the inherent vibration characteristics of the pressurized pipeline under actual operating conditions. It can identify mode shape distortions and weak areas caused by prestress and fluid influence. Full harmonic response analysis, on the other hand, directly solves the complete frequency domain dynamic equations, simulating the dynamic response near the resonance frequency with high precision, fully considering modal coupling effects and complex boundary dynamic characteristics. The synergistic effect of these two methods significantly improves the accuracy of the calculations, providing reliable theoretical support for the safety assessment, structural optimization, and risk warning of pressurized pipelines, effectively reducing vibration-induced failures and safety risks.

[0050] This invention loads multiple real loads during vibration mode calculation, accurately obtains the distribution and frequency of multi-order vibration modes, and performs full harmonic response calculation to accurately simulate the response of the pressurized pipeline under actual excitation. It can effectively find the deformation and stress conditions during vibration, providing high-precision data support for the design optimization, fault diagnosis and safety assessment of pressurized pipelines, and can significantly improve the safety and stability of the operation of pressurized pipelines in gas storage injection stations.

[0051] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures pointed out in the description, claims and drawings. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a flowchart illustrating the calculation method for the vibration mode and harmonic response process of the pipeline in the pressurization zone of the gas storage facility in an embodiment of the present invention.

[0054] Figure 2 for Figure 1 Detailed flowchart of step S2;

[0055] Figure 3 for Figure 2 Detailed flowchart of step S22;

[0056] Figure 4 for Figure 1 Detailed flowchart of step S3;

[0057] Figures 5A-5B The deformation distribution diagram and strain distribution diagram of the prestress analysis of the pipeline in the pressurization zone of the gas storage tank in this embodiment of the invention are shown respectively.

[0058] Figures 6A-6J The first to tenth order vibration mode deformation distribution diagrams of the pipeline in the pressurization zone of the gas storage tank in the embodiment of the present invention are shown respectively.

[0059] Figure 7 for Figure 1 Detailed flowchart of step S4;

[0060] Figure 8 This is a frequency response curve diagram of the fully harmonic response analysis of the gas storage pressurization zone pipeline in an embodiment of the present invention;

[0061] Figure 9A and Figure 9B The figures show the stress and deformation distribution at 14Hz, respectively, based on a complete harmonic response analysis of the gas storage pressurization zone pipeline in this embodiment of the invention.

[0062] Figure 10 A schematic diagram of an electronic device according to an embodiment of the present invention is shown. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of 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, 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.

[0064] This invention proposes a method for calculating the vibration modes and harmonic response process of a pipeline in the pressurization zone of a gas storage facility, such as... Figure 1 As shown, it includes the following steps:

[0065] S1: Construct a three-dimensional model of the pressurization zone pipeline, which includes the structural features of weld structure, support structure and high-pressure vessel;

[0066] S2: Mesh the fluid domain and solid domain of the 3D model of the pressurization zone pipeline, and set corresponding constraints on the structure in the 3D model of the pressurization zone pipeline.

[0067] S3: The prestressed coupled wet modal method is used to perform fluid-structure coupled static analysis to obtain the initial prestress of the pipeline in the pressurization zone. Based on the initial prestress, the multi-order vibration wet modes of the pipeline in the pressurization zone are calculated by combining the dynamic equations.

[0068] S4: Based on the analysis results of multi-order vibration wet modes, an external excitation load matching the actual working conditions is applied, and dynamic analysis is performed using the direct complete harmonic response method to obtain the deformation distribution and stress concentration of the pipeline during vibration in the pressurization zone.

[0069] In one embodiment of the present invention, the three-dimensional model of the pressurization zone pipeline in step S1 is established proportionally using three-dimensional modeling software based on the actual dimensions of the pressurization zone pipeline. Specifically, the actual dimension data of the pressurization zone pipeline includes pipe diameter, wall thickness, length, support location, weld location, and connection method with the high-pressure vessel. For example, during the modeling process, the shape and size of the weld are accurately drawn, and the geometric model of the support structure is constructed; the connection between the high-pressure vessel (including the oil separator and scrubbing tank) and the pressurization zone pipeline is accurately simulated to ensure the realism and accuracy of the model.

[0070] In one embodiment of the present invention, such as Figure 2 As shown, step S2 includes the following steps:

[0071] S21: Mesh the fluid domain and solid domain of the 3D model of the pressurization zone pipeline respectively;

[0072] S22: Set constraints on the structure in the 3D model of the pressurized pipeline, including elastic constraints at the clamp supports, fixed or displacement constraints at the flanges, and elastic constraints on the walls and the ground.

[0073] In one embodiment of the present invention, in step S21, the fluid domain is divided using a tetrahedral mesh, and a boundary layer mesh is set in the region near the pipe wall. For regions in the fluid domain with large velocity variations and near the pipe wall (e.g., bends in the pressurization zone pipes, near valves), local mesh refinement is performed to improve mesh quality and calculation accuracy.

[0074] The solid domain is divided using a combination of hexahedral meshes as the primary method and tetrahedral meshes as a secondary method. The solid domain of the pressurized pipeline includes, but is not limited to, the pipeline body, welds, supporting structures, flanges, etc. Local mesh refinement is performed at the connection points between the welds and supports and the pressurized pipeline to accurately simulate stress concentration at these critical locations.

[0075] In step S22, the constraint conditions at the clamp are determined by the stiffness coefficient at the clamp. The stiffness coefficient at the clamp is determined as follows: Figure 3 As shown, it includes the following steps:

[0076] S221: Collect mechanical property data of the contact materials between the pressurization zone pipeline and the clamp, and establish a calculation model of the reaction force-deformation relationship between the clamp and the pressurization zone pipeline based on the mechanical property data;

[0077] S222: Calculate the preload of a single bolt on a clamp based on the empirical formula for preload of carbon steel bolts;

[0078] S223: Based on the pre-tightening force calculation results, the compressive stress distribution on the contact surface between the clamp and the pressurized pipeline is obtained through contact mechanics analysis, and the positive pressure under the initial compressive state is determined;

[0079] S224: Based on the X, Y, and Z spatial coordinate axes, apply unidirectional stepwise displacement to the pressurization zone pipeline under the initial compression state, record the reaction force of the clamp on the pressurization zone pipeline, and plot the force-deformation curves in each direction;

[0080] S225: Calculate the stiffness coefficients (Kx, Ky, Kz) in the corresponding coordinate axis directions by the slope of the linear segment of the force-deformation curve in each direction, and use the stiffness coefficients as elastic constraint conditions at the clamp support.

[0081] In step S221, the materials in contact with the clamp include the steel of the pressurized zone pipe and the rubber pad; the mechanical property data of the pressurized zone pipe include, but are not limited to, yield strength, tensile strength, elastic modulus, Poisson's ratio, elongation, and density.

[0082] In step S222, the empirical formula for the preload of carbon steel bolts is as follows:

[0083]

[0084] In the formula: The preload force for a single bolt; Where is the yield strength of the bolt material, in MPa; As is the stress cross-sectional area of ​​the bolt. .

[0085] In step S223, in the X, Y, Z spatial coordinate axes, X is the axial direction of the pressurization zone pipeline, Y is the horizontal radial direction, and Z is the vertical radial direction.

[0086] In one embodiment of the present invention, the specific process of step S224 is as follows:

[0087] Apply an upward Z-direction displacement (e.g., 0.1mm, 0.2mm, 0.3mm, within the elastic deformation range) to the pipeline in the pressurization zone, and record the clamp reaction force (Z-direction reaction force Fz) corresponding to each displacement.

[0088] Plot the Z-axis force-deformation curve, and then plot the Y-axis force-deformation curve in the same way.

[0089] Determine the friction coefficient between the pressurization zone pipeline and the rubber pad, apply X-direction displacement to the pressurization zone pipeline, at which time the reaction force includes the reaction force of the clamp and the friction force of the rubber pad, calculate the relationship between its X-direction displacement and the total reaction force (reaction force of the clamp + friction force of the rubber pad), and plot the X-direction force-deformation curve.

[0090] In step S2, the constraints at the flange are determined according to the position of the flange, and can be divided into two types: fixed constraints and displacement constraints.

[0091] If the flange is in contact with the ground or wall, a fixed constraint is applied, or the constraint at the flange connected to the high-pressure vessel is set as a fixed constraint, restricting its six degrees of freedom.

[0092] If the flange is suspended, appropriate displacement constraints are applied. For example, for a flange connection in the middle of a pressurized pipeline, if the design allows for a certain axial displacement to compensate for deformations such as thermal expansion, axial displacement constraints are applied, allowing free deformation in the radial and circumferential directions.

[0093] In step S2, the constraints on the pressurization zone pipelines by the wall and the ground are set as elastic constraints.

[0094] In one embodiment of the present invention, such as Figure 4 As shown, step S3 includes the following steps:

[0095] S31: Apply static loads to the fluid and solids in the pressurization zone pipeline, the static loads including the fluid pressure inside the pipe, the fluid gravity, the weight of the pressurization zone pipeline, and the bolt preload and frictional resistance of the supporting constraints;

[0096] S32: Perform fluid-structure interaction static analysis based on the applied static load to calculate the initial prestress of the pipeline in the pressurization zone under static load;

[0097] S33: Map the initial prestress onto the three-dimensional model of the pressurized pipeline and use the dynamic equations to calculate the multi-order wet vibration modes of the pressurized pipeline.

[0098] In step S31, the fluid pressure inside the pipe is determined based on the actual delivery pressure, the fluid gravity is calculated based on the fluid density and the fluid volume inside the pressurization zone pipe, the gravity of the pressurization zone pipe is calculated based on the density and volume of the pressurization zone pipe material, and the preload of the bolt is calculated based on the yield strength of the bolt material and the cross-sectional area of ​​the bolt stress.

[0099] The fluid density is calculated using the following formula:

[0100]

[0101] In the formula: Fluid density (kg / m³) 3 P is the absolute pressure (in Pa); M is the molar mass of the fluid (kg / mol), i.e., the molar mass of the gas being transported; Z is the compressibility factor; R is the gas constant. T represents the thermodynamic temperature (K) of the fluid.

[0102] In one embodiment of the present invention, the calculation result of step S32 is as follows: Figure 5A (deformation distribution) and Figure 5B(Stress distribution) is shown. The results show that under the action of fluid pressure, fluid gravity, and the gravity of the pipeline in the pressurization zone, the maximum deformation is 1.02 mm, located at the elbow of the compressor secondary outlet pipeline and the elbow of the pipeline from the air cooler to the oil separator; the maximum prestress is 70.014 MPa, located near the compressor wash tank, and at the elbow of the pipeline from the air cooler to the oil separator, the stress is 50.012 MPa, and its impact on the long-term operational reliability of the pipeline needs to be considered.

[0103] The analysis results provide clear directions for subsequent optimization. For example, for elbows with concentrated deformation, the influence of secondary flow can be reduced by optimizing the radius of curvature and adding a flow guide bushing. For stress concentration interfaces, a gradual transition section and enhanced weld joint toughness are required to weaken the peak mechanical response from the structural design level and improve the long-term operational reliability of the system.

[0104] In step S33, the multi-order wet vibration modes of the pressurized pipeline are calculated, including solving for the natural frequencies of the pipeline. Based on this, the resonant frequencies of the pipeline can be found, thus avoiding the influence of the resonant frequencies on the structure. For any pressurized pipeline, the dynamic equations are as follows:

[0105]

[0106] In the formula: This is the mass matrix of the pressurized pipeline, reflecting the inertial characteristics of the pipeline, fluid, and accessories in the pressurized area. This is the damping coefficient matrix of the pipeline in the pressurization zone; This is the pipeline stiffness matrix in the pressurization zone, which includes the pipeline's own stiffness and the stiffness variation caused by the initial prestress. Indicates displacement. Indicates speed, Indicates acceleration. Let t represent time, and t be the excitation load. This formula is the classic differential equation of motion (i.e., the dynamic equation) for a multi-degree-of-freedom linear dynamic system, describing the excitation load. Under the influence of mass, damping, and stiffness, the structure of the pressurized pipeline in the pressurization zone exhibits dynamic response.

[0107] In one embodiment of the present invention, the first 10 modal distributions and frequencies of the pressurized pipeline are calculated, and the results are as follows: Figures 6A-6J As shown, the largest deformation of the first mode is located at the bend of the air cooler return pipeline; the largest deformation of the second mode is located at the bend of the compressor secondary inlet pipeline; the largest deformation of the third mode is located at the bend of the compressor secondary outlet pipeline; the largest deformation of the fourth mode is located at the bend of the compressor primary outlet pipeline; the largest deformation of the fifth, sixth, and ninth modes is located at the valve of the air cooler return pipeline; the largest deformation of the seventh and eighth modes is located at the top of the washing tank; and the largest deformation of the tenth mode is located at the air cooler return pipeline.

[0108] In one embodiment of the present invention, such as Figure 7 As shown, step S4 includes the following steps:

[0109] S41: Based on the natural frequency range in the multi-order vibration wet mode results, determine the frequency range and characteristics of the excitation load, and apply the corresponding excitation load within this frequency range;

[0110] S42: Based on the material and structural characteristics of the pressurized zone pipeline, determine the damping coefficient of the pressurized zone pipeline during normal operation that matches the excitation frequency range;

[0111] S43: Solve the dynamic equations based on the excitation load and damping coefficient, perform direct full harmonic response calculations, and determine the deformation and stress distribution of the pressurized pipeline during vibration.

[0112] S44: Extract the maximum deformation value of the pipeline in the pressurization zone and the stress concentration value in the dangerous area at the resonant frequency, analyze whether the maximum deformation value exceeds the safety limit and whether the stress exceeds the material fatigue limit, and confirm the resonance risk.

[0113] In step S41, the basic formula for applying the excitation load is:

[0114]

[0115] In the formula: F(t) is the instantaneous load amplitude at time t; F0 is the peak load. ω is the angular frequency (rad / s). , f Frequency (Hz); Given the initial phase angle (rad), calculate the deformation and stress distribution of the pipeline in the pressurization zone during vibration.

[0116] In step S42, the damping parameters can be determined by referring to material manuals or experimental data based on the material properties of the pressurized pipeline (such as carbon steel or alloy steel) and the type of support structure (such as metal brackets or rubber pads).

[0117] In one embodiment of the present invention, by extracting the swept frequency response curve at the flange of the gas storage tank, the magnitude of the amplitude and stress amplitude at that location can be obtained, such as... Figure 8 As shown, resonance occurs at the flange of the gas storage tank at a frequency of 14Hz. Figures 9A-9B As shown, when vibration occurs at a frequency of 14Hz, the area with the largest pipeline deformation is located at the elbow of the compressor's secondary outlet pipeline, with a maximum deformation of 8.25mm. The area with the largest pipeline stress is located at the base of the gas storage tank, with a maximum stress of 1950.1Mpa.

[0118] If the compressor speed in the pressurization zone pipeline is 997 r / min, the compressor excitation frequency is 16.62 Hz, which is close to the eighth and ninth resonant frequencies. Therefore, the risk of resonance at the gas storage tank flange is relatively high. If the dry modal analysis method is used, the vibration modal frequency of the pipeline system will be significantly reduced because the influence of fluid and prestress is ignored.

[0119] Through the above implementation steps, the vibration modes of the pressurization zone pipeline of the gas storage and injection station and the vibration response characteristics under specific excitation loads can be accurately obtained. The calculation results are compared with the actual test data, and the error is within 5%, indicating that the calculation method of the present invention has high accuracy and reliability.

[0120] Based on the same inventive concept, this invention proposes a calculation system for the mode shape and harmonic response process of a pipeline in the pressurization zone of a gas storage facility, comprising:

[0121] The 3D model building module is used to build a 3D model of the pressurization zone pipeline. The 3D model of the pressurization zone pipeline is a scaled model, including the geometric features and connection methods of welds, supports, and high-pressure vessels.

[0122] The mesh generation and constraint setting module is used to mesh the fluid domain and solid domain of the 3D model of the pressurization zone pipeline, and to set corresponding constraints on the structure in the 3D model of the pressurization zone pipeline.

[0123] The fluid-structure interaction static and wet modal analysis module is used to perform fluid-structure interaction static analysis using the prestressed coupled wet modal method to obtain the initial prestress of the pipeline in the pressurization zone. Based on the initial prestress, the module uses dynamic equations to calculate the multi-order vibration wet modes of the pipeline in the pressurization zone.

[0124] The Full Harmonic Response Analysis and Resonance Assessment Module is used to apply external excitation loads that match the actual working conditions based on the analysis results of multi-order vibration wet modes, and to perform dynamic analysis using the direct full harmonic response method to obtain the deformation distribution and stress concentration of the pipeline during vibration in the pressurization zone.

[0125] Another exemplary embodiment of the present invention provides an electronic device. For example... Figure 10 As shown, the electronic device includes at least one processor 1001, at least one communication interface 1002, at least one memory 1003 and at least one communication bus 1004; wherein the processor 1001, the communication interface 1002 and the memory 1003 communicate with each other through the communication bus 1004.

[0126] Memory 1003 stores computer programs;

[0127] The processor 1001, when executing the program stored in the memory 1003, implements a method for calculating the mode shape and harmonic response process of the pipeline in the pressurization zone of the gas storage tank.

[0128] Optionally, the communication interface can be an interface of a communication module, such as the interface of a GSM module; the processor may be a CPU, an Application Specific Integrated Circuit (ASIC), or one or more integrated circuits configured to implement embodiments of the present invention. The memory may include high-speed RAM and may also include non-volatile memory, such as at least one disk storage device. The memory stores a program, and the processor calls the program stored in the memory to execute some or all of the above-described method embodiments.

[0129] Based on the same inventive concept, embodiments of this application also provide a computer-readable storage medium storing a computer program, which, when executed, implements some or all of the above-described method embodiments. Optionally, the storage medium may be a non-transitory computer-readable storage medium, such as a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, and optical data storage device.

[0130] Based on the same inventive concept, embodiments of this application also provide a computer program product, including a computer program / instructions, which are executed by a processor of some or all of the above-described method embodiments.

[0131] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the mode shape and harmonic response process of a pipeline in the pressurization zone of a gas storage facility, characterized in that, Includes the following steps: Mesh the fluid and solid domains of the 3D model of the pressurization zone pipeline, and set corresponding constraints on the structure in the 3D model of the pressurization zone pipeline. The prestressed coupled wet modal method is used to perform fluid-structure coupled static analysis to obtain the initial prestress of the pipeline in the pressurization zone. Based on the initial prestress, the multi-order vibration wet modes of the pipeline in the pressurization zone are calculated using dynamic equations. Based on the analysis results of multi-order vibration wet modes, an external excitation load matching the actual working conditions is applied, and dynamic analysis is performed using the direct complete harmonic response method to obtain the deformation distribution and stress concentration of the pipeline vibration in the pressurization zone. The steps include: based on the natural frequency range in the multi-order vibration wet mode results, the frequency range and characteristics of the excitation load are determined, and an excitation load with corresponding characteristics is applied within this frequency range. Based on the material and structural characteristics of the pressurized pipeline, determine the damping coefficient of the pressurized pipeline during normal operation that matches the excitation frequency range; Based on the excitation load and damping coefficient, the dynamic equation is solved, and the direct full harmonic response is calculated to determine the deformation and stress distribution of the pressurized pipeline during vibration. Extract the maximum deformation value of the pipeline in the pressurization zone and the stress concentration value in the dangerous area at the resonant frequency, analyze whether the maximum deformation value exceeds the safety limit and whether the stress exceeds the material fatigue limit, and confirm the resonance risk.

2. The method for calculating the vibration mode and harmonic response process of the pipeline in the pressurization zone of a gas storage facility according to claim 1, characterized in that, The three-dimensional model of the pressurization zone pipeline is a scaled model, including the geometric features and connection methods of welds, supports, and high-pressure vessels.

3. The method for calculating the vibration mode and harmonic response process of the pipeline in the pressurization zone of a gas storage facility according to claim 1, characterized in that, The fluid domain is divided using a tetrahedral mesh, with a boundary layer mesh set in the region near the pipe wall; The solid domain is divided using a combination of hexahedral meshes as the primary method and tetrahedral meshes as the secondary method, with local mesh refinement at welds, supports, and high-pressure vessel connections.

4. The method for calculating the mode shape and harmonic response process of the pipeline in the pressurization zone of a gas storage facility according to any one of claims 1-3, characterized in that, The constraints include elastic constraints at the clamp supports, fixed or displacement constraints at the flanges, and elastic constraints on the walls and the ground.

5. The method for calculating the vibration mode and harmonic response process of the pipeline in the pressurization zone of a gas storage facility according to claim 4, characterized in that, The elastic constraint at the clamp support is determined according to the following steps: Collect mechanical property data of the contact materials between the pipeline and the clamp in the pressurization zone, and establish a calculation model of the reaction force-deformation relationship between the clamp and the pipeline in the pressurization zone based on the mechanical property data; Calculate the preload of a single bolt on the clamp based on the empirical formula for preload of carbon steel bolts; Based on the pre-tightening force calculation results, the compressive stress distribution on the contact surface between the clamp and the pressurized pipeline is obtained through contact mechanics analysis, and the positive pressure under the initial compressive state is determined. Based on the X, Y, and Z spatial coordinate axes, unidirectional stepwise displacement is applied to the pipeline in the pressurization zone under the initial compression state. The reaction force of the clamp on the pipeline in the pressurization zone is recorded, and the force-deformation curves in each direction are plotted. The stiffness coefficients in the corresponding coordinate axis directions are calculated by the slope of the linear segment of the force-deformation curves in each direction, and these stiffness coefficients are used as elastic constraint conditions at the clamp support.

6. The method for calculating the vibration mode and harmonic response process of the pipeline in the pressurization zone of a gas storage facility according to claim 1, characterized in that, The type of constraint at the flange is determined by the flange's connection relationship. If the flange is in contact with the ground, wall, or high-pressure vessel, a fixed constraint is applied; if the flange is suspended, a displacement constraint is applied.

7. The method for calculating the vibration mode and harmonic response process of the pipeline in the pressurization zone of a gas storage facility according to claim 1, characterized in that, The method employs a prestressed coupled wet modal approach to perform fluid-structure coupled static analysis, obtaining the initial prestress of the pipeline in the pressurization zone. Based on this initial prestress, the multi-order wet vibration modes of the pipeline in the pressurization zone are calculated using dynamic equations, including the following steps: The static loads of the fluid and solids in the pressurization zone pipeline are applied, including the fluid pressure inside the pipe, the fluid gravity, the gravity of the pressurization zone pipeline, and the preload and frictional resistance of the bolts supporting the constraint. Based on the applied static load, a fluid-structure interaction static analysis is performed to calculate the initial prestress of the pipeline in the pressurization zone under static load. The initial prestress is mapped onto the three-dimensional model of the pipeline in the pressurization zone, and the multi-order wet vibration modes of the pipeline in the pressurization zone are calculated using dynamic equations.

8. The method for calculating the vibration mode and harmonic response process of the pipeline in the pressurization zone of a gas storage facility according to claim 7, characterized in that, The fluid pressure inside the pipe is determined based on the actual delivery pressure. The fluid gravity is calculated based on the fluid density and the fluid volume in the pressurized zone pipe. The gravity of the pressurization zone pipeline is calculated based on the density and volume of the pipeline material in the pressurization zone. The preload of the bolt is calculated based on the yield strength of the bolt material and the cross-sectional area of ​​the bolt stress.

9. The method for calculating the mode shape and harmonic response process of the pipeline in the pressurization zone of a gas storage facility according to claim 1, characterized in that, The excitation load satisfies the following formula: In the formula: F(t) is the instantaneous load amplitude at time t; F0 represents the peak load. Angular frequency, =2 f , f For frequency; This is the initial phase angle.

10. A calculation system for the mode shape and harmonic response process of a pipeline in the pressurization zone of a gas storage facility, characterized in that, include: The mesh generation and constraint setting module is used to mesh the fluid domain and solid domain of the 3D model of the pressurization zone pipeline, and to set corresponding constraints on the structure in the 3D model of the pressurization zone pipeline. The fluid-structure interaction static and wet modal analysis module is used to perform fluid-structure interaction static analysis by coupling fluid loads and solid loads using the prestressed coupled wet modal method, to obtain the initial prestress of the pipeline in the pressurization zone, and to calculate the multi-order vibration wet modes of the pipeline in the pressurization zone using dynamic equations; The Full Harmonic Response Analysis and Resonance Assessment Module is used to apply external excitation loads that match the actual working conditions, and to perform dynamic analysis using the direct full harmonic response method to obtain the deformation distribution and stress concentration of the pipeline during vibration in the pressurization zone. The module includes the following steps: based on the natural frequency range in the multi-order vibration wet mode results, determine the frequency range and characteristics of the excitation load, and apply the corresponding excitation load within the frequency range. Based on the material and structural characteristics of the pressurized pipeline, determine the damping coefficient of the pressurized pipeline during normal operation that matches the excitation frequency range; Based on the excitation load and damping coefficient, the dynamic equation is solved, and the direct full harmonic response is calculated to determine the deformation and stress distribution of the pressurized pipeline during vibration. Extract the maximum deformation value of the pipeline in the pressurization zone and the stress concentration value in the dangerous area at the resonant frequency, analyze whether the maximum deformation value exceeds the safety limit and whether the stress exceeds the material fatigue limit, and confirm the resonance risk.

11. The calculation system for the mode shape and harmonic response process of the pipeline in the pressurization zone of a gas storage facility according to claim 10, characterized in that, The system also includes a 3D model building module for building a 3D model of the pressurization zone pipeline; The three-dimensional model of the pressurization zone pipeline is a scaled model, including the geometric features and connection methods of welds, supports, and high-pressure vessels.

12. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a method for calculating the mode shape and harmonic response process of the gas storage pressurization zone pipeline as described in any one of claims 1-9.

13. A computer program product comprising a computer program / instructions, characterized in that, When executed by a processor, the computer program / instruction implements the method for calculating the mode shape and harmonic response process of the gas storage pressurization zone pipeline as described in any one of claims 1-9.

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