A fast identification method of acoustic coupling modes of a main pipe-closed side branch pipe

Abstract

This invention relates to a rapid identification method for acoustic coupling modes of a main pipe and a closed-side branch pipe. The method involves constructing geometric models of the main pipe and the closed-side branch pipe; establishing an acoustic transfer matrix based on the acoustic transfer equation of a uniform straight pipe using the transfer matrix method; correcting the input impedance at the branch pipe opening by combining end correction coefficients and three-dimensional effect correction coefficients; substituting the boundary conditions at the connection point and combining them with the boundary conditions at both ends of the main pipe to derive the characteristic equation; solving it numerically to obtain the characteristic frequencies of the coupling modes; and determining the mode type of the characteristic frequencies by utilizing the relationship between the dimensionless contribution factors of the main pipe and the branch pipe based on the obtained characteristic frequencies. This invention significantly improves efficiency while ensuring computational accuracy, accurately identifies the coupling mode type, and guides the design of frequency misalignment and resonance risk assessment of pipeline systems.

Description

Technical Field

[0001] This invention relates to the field of flow-induced acoustic resonance analysis technology for pipeline systems, specifically to a rapid identification method for acoustic coupling modes of the main pipe and the closed-side branch pipe. Background Technology

[0002] In large pipeline systems such as main steam pipelines and chemical transmission pipelines in nuclear power plants, closed-loop branch pipe structures formed by safety relief valves and bypass valves are often installed. When high-temperature, high-pressure fluids flow through the connection between the main pipe and the branch pipe, a shear layer forms at the upstream edge of the branch pipe opening, generating periodic vortex shedding. When the frequency of vortex shedding approaches the acoustic natural frequency of the branch pipe or main pipe, it can excite strong flow-induced acoustic resonance, causing a sharp increase in sound pressure inside the pipe. In severe cases, this can lead to structural acoustic fatigue failure, endangering the safe operation of the system.

[0003] Accurately predicting the acoustic coupling mode frequencies of the main pipe-branch pipe system is a crucial prerequisite for designing pipe frequencies that could lead to resonance. In existing technologies, acoustic modal analysis of isolated branch pipes typically employs one-dimensional acoustic theory formulas for estimation. However, when the main pipe and branch pipes are connected to form a system, sound waves undergo reflection, transmission, and energy redistribution at the connection points. The acoustic modes of the main pipe itself may strongly couple with those of the branch pipes, forming system-level acoustic resonance modes. The frequencies and mode shapes of these coupled modes cannot be obtained through simple superposition of isolated components; a full system analysis is necessary.

[0004] Currently, the analysis of acoustic coupling modes in main-branch pipe systems mainly relies on three-dimensional finite element acoustic numerical simulation (such as software like COMSOL and ANSYS). For example, the paper "Research and Optimization of Flow-Acoustic Coupling Characteristics of Closed Side Branch Pipelines" by Yin Wenhui, published in the China Excellent Master's Thesis Full-text Database, Engineering Technology II, 2024, No. 04, pp. 23-59, April 15, 2024, discloses a study on the flow-acoustic coupling characteristics of closed side branch pipes using software numerical simulation; or the patent CN121435584A, "Analysis Method, System and Computer-Readable Medium for Pipeline Acoustic Vibration," significantly shortens modeling time and improves the efficiency of calculating the natural frequency of acoustic vibration through automatic dimensionality reduction and one-dimensional modeling; based on the error comparison between the natural frequency and the fluid / solid frequency, it accurately identifies the risks of flow-acoustic coupling and acoustic-solid coupling, enhancing the safety of pipeline design. While these methods can yield relatively accurate results, they have the following drawbacks: First, the workload of 3D modeling and mesh generation is large, and the calculation cycle is long (from several hours to several days), making them unsuitable for rapid iteration in the preliminary design stage of engineering projects. Second, they consume a lot of computing resources, which is difficult to handle for multi-condition scanning analysis of large-scale pipeline systems. Third, they lack clear physical meaning and it is difficult to intuitively determine the modal type (branch-dominated, main-dominated, or strongly coupled).

[0005] Based on this, the present invention proposes a rapid identification method for the acoustic coupling modes of the main pipe and branch pipe, aiming to establish a rapid prediction model of the acoustic coupling modes of the system and provide an efficient tool for pipeline resonance risk assessment. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a rapid identification method for the acoustic coupling modes of the main pipe and the closed-side branch pipe to solve the above problems.

[0007] This invention provides the following technical solution: A rapid identification method for acoustic coupling modes of a main pipe and a closed side branch pipe includes the following steps: Construct geometric models of the main pipe and the closed side branches; Based on the acoustic transfer equation of a uniform straight pipe, the acoustic transfer matrices of the main pipe and branch pipes are established respectively using the transfer matrix method. The end correction factor is determined based on the ratio of the inner diameter of the branch pipe to that of the main pipe, and the three-dimensional effect correction factor is determined based on the geometry of the connection. The input impedance of the branch pipe opening is corrected by combining the end correction factor and the three-dimensional effect correction factor. Substituting the modified input impedance of the branch pipe opening into the boundary conditions at the connection, and combining it with the boundary conditions of the openings at both ends of the main pipe, the characteristic equation is derived. The characteristic frequency of the coupled mode is obtained by solving it using numerical methods. Based on the obtained characteristic frequencies, the dimensionless contribution factors of the main pipe and branch pipes are used. and The magnitude relationship is used to determine the mode type of the characteristic frequencies.

[0008] Preferably, the characteristic equation is as follows: ; Among them, the dimensionless area ratio ; These are the diameters of the main pipe and the straight pipe, respectively; For wave number, Divide the main pipe into left and right sections according to the connection point: left section length Length of the right segment ; This is the correction coefficient for three-dimensional effects; For effective acoustic length.

[0009] Preferably, the effective acoustic length for:

[0010] in, branch pipe length End correction factor.

[0011] Preferred contribution factors from supervisors Contribution factors of branches The formula is as follows: ; .

[0012] Preferably, the modal types include branch-dominant, main-dominant, and main-branch strongly coupled types; The branch-dominant type: The characteristic frequency is close to the natural frequency of the branch pipe; The so-called manager-led type: The characteristic frequency is close to the natural frequency of the main tube; The main-branch strongly coupled type: and Neither is close to zero; the sound energy is significantly distributed in both the main pipe and the branch pipes.

[0013] Preferably, the branch pipe is installed vertically on the main pipe, with an end correction factor. The value ranges from 0.3 to 0.425; for right-angle connections, Three-dimensional effect correction coefficient Take a value between 0.1 and 0.2; for rounded corner connections, the three-dimensional effect correction factor is... It decreases as the fillet radius increases.

[0014] Preferably, the acoustic transfer equation of the uniform straight tube is as follows: ; Where T(L) represents the acoustic transfer matrix; the pipe length is... The sound pressure and volume velocity at the pipe inlet are respectively , The sound pressure and volume velocity at the pipe outlet are respectively , ; The characteristic acoustic impedance of the pipe; For wave number, ; It represents the imaginary unit.

[0015] Preferably, the boundary conditions at the connection include the sound pressure continuity condition, the volumetric flow rate conservation condition, and the branch pipe impedance relationship.

[0016] Preferably, the numerical method for solving the problem includes the following steps: Determine the search frequency band: Estimate the possible modal frequency range based on the pipeline system structure; Coarse localization using scanning method: Within the search frequency band, using frequency steps... The sign change in the calculation; Bisection method for narrowing the interval: The interval is repeatedly narrowed using the bisection method until the interval width is less than the preset tolerance. .

[0017] Preferably, after obtaining the characteristic frequencies using numerical methods, Newton's iteration is used to improve the accuracy.

[0018] The present invention has the following beneficial technical effects: The fast identification method for acoustic coupling modes of main pipes and branch pipes provided by this invention can significantly improve efficiency while ensuring calculation accuracy, accurately identify coupling mode types, and introduce end correction and three-dimensional effect correction to control calculation errors and identify mode types, thereby guiding the misfrequency design and resonance risk assessment of pipeline systems, and providing a reliable basis for engineering design and resonance risk assessment. Attached Figure Description

[0019] Figure 1 This is the geometric model of the main pipe-closed side branch structure of the present invention; Figure 2 This is the calculation model for the main pipe-closed side branch structure of the present invention. Detailed Implementation

[0020] 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, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] The study found that, under plane wave propagation conditions, the acoustic characteristics of the main pipe and branch pipes can be described by transfer matrices, and the compatibility conditions at the connection points can be used to establish the system's characteristic equations. Solving these characteristic equations allows for the rapid acquisition of the system's coupled modal frequencies. Introducing end-point corrections and three-dimensional effect corrections significantly improves computational accuracy.

[0022] Example: A rapid identification method for acoustic coupling modes of main pipe-closed side branch pipes is proposed, which can be used for resonance risk assessment and optimization design of pipelines in engineering projects such as nuclear power plants, chemical plants, and water pipelines. Figures 1-2 As shown, this method, based on acoustic transfer matrix theory, models the main pipe and branch pipes separately, applies compatibility conditions at the connection points to establish the system characteristic equation, and introduces end corrections and three-dimensional effect corrections. The coupled modal frequencies are obtained by solving the characteristic equation, and the modal types are identified based on the eigenvector distribution. Specifically, it includes the following steps: Step 1: Establish the governing equations for one-dimensional plane waves Consider a plane wave propagating inside a rigid-walled circular pipe in a uniform, stationary fluid. Assume that only a one-dimensional wave propagates axially within the pipe, and that its frequency is lower than the cutoff frequency of the pipe's first-order non-plane wave. Then the sound pressure and axial particle velocity Depends only on axial coordinates Introducing volume velocity ;in Let c be the cross-sectional area of ​​the pipe, c represent the speed of sound in the fluid, and D represent the diameter of the pipe cavity.

[0023] For simple harmonic waves (time factor) The sound pressure and volume velocity satisfy the following system of differential equations:

[0024] This expression can be written in matrix form:

[0025] in, For fluid density, Speed ​​of sound; Angular frequency; For frequency; It is an imaginary number.

[0026] Step 2: Derive the acoustic transfer matrix of a uniform straight tube Apply equation (1) to Differentiating and substituting into equation (2), we get:

[0027] in Wave number (unit: The general solution of equation (4) is:

[0028] in Indicates a traveling wave propagating to the right. represents a traveling wave propagating to the left; e represents the Euler number.

[0029] Combine equations (1) and (5), and use... The solution can be found :

[0030]

[0031] in The characteristic acoustic impedance of the pipe. ;then:

[0032] Let the length of the pipe be... Pipe inlet ( The sound pressure and volume velocity at point ) are respectively , ,exit( The sound pressure and volume velocity at point ) are respectively , Substituting these equations into equations (5) and (6), we obtain:

[0033] Substitute equations (7) and (8) into equations (9) and (10); And using Euler's formula Rearranging into matrix form, we get:

[0034] Equation (11) is the acoustic transfer equation for a uniform straight pipe. That is, the acoustic transfer matrix.

[0035] Step 3: Establish the acoustic transfer matrix for the main pipe and branch pipes. like Figure 1 In the main pipe with closed side branch structure of the present invention, the main pipe is a uniform straight pipe with open ends, and the branch pipe is a uniform straight pipe with one end closed and the other end open. Therefore, the acoustic transmission matrix of the main pipe and the branch pipe can be obtained according to equation (11).

[0036] Let the total length of the supervisor be... , inner diameter Cross-sectional area The characteristic acoustic impedance of the main body Its acoustic transfer matrix is ​​given by equation (11), denoted as . For the supervisor segment, when considering a length of... When the pipe section is in use, its transfer matrix is: ,in For any length of the main pipe section.

[0037] Branch pipe length is , inner diameter b Cross-sectional area Characteristic acoustic impedance of branch pipe The sound pressure and volume velocity at the closed end of the branch pipe are respectively... , ,in The sound pressure and volume velocity at the branch pipe opening are respectively , A branch pipe is for pipes that open from the end ( ) to the closed end ( The acoustic unit of ) is obtained from equation (11):

[0038] The input impedance at the branch pipe opening can be obtained from the second line of equation (12). :

[0039] Step 4: End-point correction and 3D effect correction In one-dimensional theory, the reflection of sound waves at the open end occurs at the physical port. However, in reality, due to the radiation inertia of the port, the antinodes of the sound pressure wave are slightly offset outward, requiring an additional correction length to be added to the branch pipe length. For branch pipes installed vertically on the main pipe, the end correction factor is related to the diameter ratio, denoted as... Effective acoustic length for:

[0040] Among them, the end correction coefficient The value ranges from 0.3 to 0.425; The corrected input impedance at the branch pipe opening is:

[0041] At the main-branch connection, due to the abrupt geometric change, even at frequencies lower than the main cutoff frequency, non-propagating higher-order modes will be excited at the connection. While these modes do not propagate over long distances, they store acoustic energy locally, manifesting as an additional acoustic mass, thus affecting the acoustic impedance at the connection point. A three-dimensional effect correction factor is introduced. Then, the input impedance of the branch pipe opening after end correction and three-dimensional effect correction is:

[0042] For right-angle connections, Take 0.1 to 0.2; for rounded corner connections, The value ranges from 0 to 0.15, and decreases as the fillet radius increases; Step 5: Establish the system characteristic equation Based on the connection point between the branch pipe and the main pipe, the main pipe is divided into left and right sections: left section length Length of the right segment ,satisfy .set up , and The left side of the supervisor ( ), at the connection point of the main and side pipes ( ) and the right section of the supervisor ( The sound pressure at that location and These are the volume velocities at the left and right ends of the main pipe, respectively. and These represent the volume velocities flowing from the left side into the connection point and from the connection point to the right side, respectively. Both ends of the main pipe are open boundaries, meaning the sound pressure is zero.

[0043] The transmission relationship from the left end of the main pipe to the connection point is as follows:

[0044] The transmission relationship from the connection point to the right end of the main pipe is as follows:

[0045] At the connection point, based on the conditions of sound pressure continuity, volumetric flow conservation, and branch pipe impedance, we can obtain:

[0046] Solving equations (17) and (18) simultaneously yields:

[0047] Therefore, the solution is... and Relationship:

[0048] Similarly, by combining equations (17) and (19), we can solve for... and Relationship:

[0049] Substituting equations (22) and (23) into equation (21) and eliminating non-zero values... After sorting, we get:

[0050] Substitution ,use , We can obtain:

[0051] Both sides ride together and noticed After sorting, we get:

[0052] Denote the dimensionless area ratio ,but Therefore, the final characteristic equation is:

[0053] When the connection point is located in the middle of the main pipe Equation (26) can be simplified to:

[0054] Step 6: Numerical solution of the characteristic equation The characteristic equation (26) is a transcendental equation and needs to be solved numerically. The solution steps are as follows: Step 1: Determine the search frequency band. Estimate the possible modal frequency range based on the piping system structure. Branch fundamental frequency. Approximately (Unit: Hz), main frequency Approximately (Unit: Hz). Search frequency band selection .

[0055] Step 2: Coarse localization using the scanning method. Within the search frequency band, the frequency step size is... (Unit: Hz) The sign change of the calculation, where The left-hand side of expression (26) is represented. When At that time, there exists a root within that interval; where, and Representing functions respectively At frequency point and The calculated value at that location.

[0056] Step 3: Narrowing the Interval Using the Bisection Method. For each rooted interval, repeatedly narrow the interval using the bisection method until the interval width is less than the preset tolerance. The obtained characteristic frequencies can be further improved with Newton-Raphson iteration.

[0057] Step 7: Modality Type Identification After obtaining the characteristic frequencies, it is necessary to determine the corresponding mode types. Define dimensionless quantities. , These are the supervisor's contribution factor and the branch's contribution factor, respectively: ,

[0058] The characteristic equation can now be written as: Available and The size relationship helps determine the modality type: when When the absolute value is very small (i.e.) At this point, the branch pipe is close to the acoustic resonance state, the acoustic energy is mainly concentrated in the branch pipe, and the modal type is branch pipe dominant. when When the absolute value is very small (i.e.) At this point, the duct is close to the acoustic resonance state, the acoustic energy is mainly concentrated in the duct, and the modal type is duct-dominated. when and When neither is close to zero, the two match each other, and the acoustic energy is significantly distributed in both the main pipe and the branch pipe. The modal type belongs to the strong coupling type of main pipe-branch pipe.

[0059] The method is validated using typical geometric parameters as an example: main pipe length. , inner diameter branch length , inner diameter Sound velocity in water medium ,density An acoustic model was established using the three-dimensional finite element simulation software COMSOL Multiphysics, and the frequencies of the first four coupled modes of the system were calculated as reference values. Using this method, the following values ​​were taken... , The results are compared below:

[0060] The calculation results show that the frequency of the coupled modes predicted by this method is in good agreement with the finite element simulation results, with relative errors all within 2%. Furthermore, the fourth strongly coupled mode was successfully identified, proving the accuracy and reliability of this method.

[0061] The embodiments described above are merely illustrative of specific implementations of the present invention, and while the descriptions are detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A rapid identification method for acoustic coupling modes of a main pipe and a closed side branch pipe, characterized in that, Includes the following steps: Construct geometric models of the main pipe and the closed side branches; Based on the acoustic transfer equation of a uniform straight pipe, the acoustic transfer matrices of the main pipe and branch pipes are established respectively using the transfer matrix method. The end correction factor is determined based on the ratio of the inner diameter of the branch pipe to that of the main pipe, and the three-dimensional effect correction factor is determined based on the geometry of the connection. The input impedance of the branch pipe opening is corrected by combining the end correction factor and the three-dimensional effect correction factor. Substituting the modified input impedance of the branch pipe opening into the boundary conditions at the connection, and combining it with the boundary conditions of the openings at both ends of the main pipe, the characteristic equation is derived. The characteristic frequency of the coupled mode is obtained by solving it using numerical methods. Based on the obtained characteristic frequencies, the dimensionless contribution factors of the main pipe and branch pipes are used. and The magnitude relationship is used to determine the mode type of the characteristic frequencies.

2. The rapid identification method for acoustic coupling modes of a main pipe-closed side branch pipe according to claim 1, characterized in that, The characteristic equation is as follows: ； Among them, the dimensionless area ratio ; These are the diameters of the main pipe and the straight pipe, respectively; For wave number, Divide the main pipe into left and right sections according to the connection point: left section length Length of the right segment ; This is the correction coefficient for three-dimensional effects; For effective acoustic length.

3. The rapid identification method for acoustic coupling modes of a main pipe-closed side branch pipe according to claim 2, characterized in that, The effective acoustic length for: in, branch pipe length End correction factor.

4. The rapid identification method for acoustic coupling modes of a main pipe-closed side branch pipe according to claim 3, characterized in that, Supervisor's contribution factor Contribution factors of branches The formula is as follows: ； 。 5. The rapid identification method for acoustic coupling modes of a main pipe-closed side branch pipe according to claim 4, characterized in that, Modal types include branch-dominant, main-dominant, and main-branch strongly coupled types; The branch-dominant type: The characteristic frequency is close to the natural frequency of the branch pipe; The so-called manager-led type: The characteristic frequency is close to the natural frequency of the main tube; The main-branch strongly coupled type: and Neither is close to zero; the sound energy is significantly distributed in both the main pipe and the branch pipes.

6. The rapid identification method for acoustic coupling modes of a main pipe-closed side branch pipe according to claim 3, characterized in that, The branch pipe is installed vertically on the main pipe, with an end correction factor. The value ranges from 0.3 to 0.425; for right-angle connections, Three-dimensional effect correction coefficient Take a value between 0.1 and 0.2; for rounded corner connections, the three-dimensional effect correction factor is... It decreases as the radius of the fillet increases.

7. The rapid identification method for acoustic coupling modes of a main pipe-closed side branch pipe according to claim 1, characterized in that, The acoustic transfer equation for the uniform straight tube is as follows: ； Where T(L) represents the acoustic transfer matrix; the pipe length is... The sound pressure and volume velocity at the pipe inlet are respectively , The sound pressure and volume velocity at the pipe outlet are respectively , ; The characteristic acoustic impedance of the pipe; For wave number, ; It represents the imaginary unit.

8. The rapid identification method for acoustic coupling modes of a main pipe-closed side branch pipe according to claim 1, characterized in that, The boundary conditions at the connection include the sound pressure continuity condition, the volumetric flow rate conservation condition, and the branch pipe impedance relationship.

9. The rapid identification method for acoustic coupling modes of a main pipe-closed side branch pipe according to claim 1, characterized in that, The numerical method for solving the problem includes the following steps: Determine the search frequency band: Estimate the possible modal frequency range based on the pipeline system structure; Coarse localization using scanning method: Within the search frequency band, using frequency steps... The sign change in the calculation; Bisection method for narrowing the interval: The interval is repeatedly narrowed using the bisection method until the interval width is less than the preset tolerance. .

10. The rapid identification method for acoustic coupling modes of a main pipe-closed side branch pipe according to claim 9, characterized in that, After obtaining the characteristic frequencies using numerical methods, Newton's iteration is used to improve the accuracy.

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