Method for calculating mass of attached water of multi-cylinder array system

Abstract

The invention discloses a method for calculating the mass of attached water of a multi-cylinder array system. The method comprises the following steps: solving the velocity potential of a flow field when a single cylinder vibrates in water; according to the velocity potential of the flow field when the single cylinder vibrates in the water, solving the velocity potential of the flow field when the double cylinders vibrate in the water; according to the velocity potential of the flow field when the double-cylinder vibrates in the water, solving the hydrodynamic force borne by the double-cylinder when the double-cylinder vibrates in the water; according to the hydrodynamic force borne by the double cylinders when the double cylinders vibrate in the water, the hydrodynamic force borne by any single cylinder when the multiple cylinders vibrate in the water is solved; and calculating the mass of the attached water of any single cylinder according to the hydrodynamic force borne by the single cylinder when the multiple cylinders vibrate in the water. Based on the potential flow theory, the invention provides the multi-cylinder array system attached water calculation method which is high in accuracy, accurate and reliable, and the accuracy and efficiency of engineering design are improved.

Description

Technical Field

[0001] The present invention relates to the field of fluid mechanics, and in particular to a method for calculating attached water mass of a multi-cylinder array system. Background Art

[0002] Nowadays, with the advancement of science and technology, the vast majority of machinery and structures operate in complex fluid environments, and their vibration characteristics are inevitably affected by the fluid. For example, turbines and impellers in fluid machinery, propellers in ships, pile foundations of offshore platforms during earthquakes, and wave energy devices all have the characteristics of cylindrical or multi-cylinder structures. In engineering, the vibration of such structures or components in water can be attributed to the fluid-structure interaction problem of multi-cylinder structures.

[0003] In multi-cylinder arrays (such as offshore platform pile foundations and wave energy devices), the interaction of attached water masses may lead to the following phenomena: Vibration resonance: The attached water masses of adjacent cylinders may form "coupled vibrations", resulting in a decrease in the system's resonant frequency or an increase in the amplitude. Vortex-induced vibration suppression: Reasonable design of cylinder spacing or additional structures (such as guide plates) can change the distribution of attached water masses, thereby suppressing vortex shedding. Energy transfer: The attached water mass affects the efficiency of diffusion of vibration energy from a single cylinder to the surrounding environment. Therefore, obtaining the accurate attached water mass of a multi-cylinder array system when it vibrates in water is crucial in engineering.

[0004] Currently, there are few literatures at home and abroad that cover this area of ​​research, and few relevant literatures report research results. Due to the lack of effective basic theoretical research results, there has been no specific solution to solve the attached water mass in multi-cylinder vibration systems. Summary of the Invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for calculating the mass of attached water in a multi-cylinder array system, which solves the problem that the prior art cannot accurately calculate the mass of attached water in a multi-cylinder array system.

[0006] In order to achieve the above-mentioned object, the technical solution adopted by the present invention is: a method for calculating the attached water mass of a multi-cylinder array system, comprising: Solve the velocity potential of the flow field when a single cylinder vibrates in water; The velocity potential of the flow field when the double cylinders vibrate in water is solved based on the velocity potential of the flow field when the single cylinder vibrates in water. The hydrodynamic force on the double cylinders when they vibrate in water is solved based on the velocity potential of the flow field when the double cylinders vibrate in water. Based on the hydrodynamic forces on the double cylinders when they vibrate in water, solve the hydrodynamic forces on any single cylinder when multiple cylinders vibrate in water; The attached water mass of any single cylinder is calculated based on the hydrodynamic force on the single cylinder when the multi-cylinder vibrates in water.

[0007] Furthermore: The velocity potential of the flow field when a single cylinder vibrates in water is:

[0008] in, represents the velocity potential of the flow field when a single cylinder vibrates in water, is the radius of a single cylinder, is the amplitude, is the angular frequency, For time, is the cosine function, is the rectangular coordinate of any point in the flow field, is the polar coordinate of any point in the flow field.

[0009] Further: the double cylinder includes a cylinder and cylinder b ; When the double cylinder vibrates in water, the velocity potential of the flow field is Velocity potential when vibrating in water ,cylinder b Velocity potential when vibrating in water and cylindrical Cylinder at rest b Vibrating in water Velocity potential generated at The linear superposition of is expressed as:

[0010]

[0011] in, is the velocity potential of the flow field when the double cylinders vibrate in water, For cylinder The radius, For cylinder b The radius, For cylinder and cylinder b The spacing between For cylinder b The polar coordinates of the center of the circle, For cylinder b The rectangular coordinates of the center of the circle; is a sine function; 、 is the intermediate parameter, is a constant whose value is a positive integer; For cylinder bVelocity potential of the flow field in polar coordinates when vibrating in water; is the ratio of pi; .

[0012] Furthermore, the hydrodynamic force exerted on the double cylinders when they vibrate in water is:

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] in, It represents the hydrodynamic force on the surface of any single cylinder parallel to the vibration direction of the cylinder when the double cylinder vibrates in water. It represents the hydrodynamic force on the surface of any single cylinder when the double cylinder vibrates in water in the direction perpendicular to the vibration direction of the cylinder; It represents the hydrodynamic pressure on any single cylinder of the double cylinder in water; represents the attached water mass coefficient parallel to the vibration direction of the double cylinder, represents the attached water mass coefficient perpendicular to the vibration direction of the double cylinder; represents the density of water, represents the mass of water per unit height of a single cylinder, is the acceleration time history of multiple cylinders vibrating in water.

[0019] Further: 、 as well as The calculation expressions are:

[0020]

[0021] For cylinder and cylinders b The center distance coefficient between .

[0022] Furthermore, when multiple cylinders vibrate in water, the hydrodynamic force on any single cylinder is the sum of the hydrodynamic forces acting on it by all other cylinders, and its calculation expression is:

[0023]

[0024] in, When multiple cylinders vibrate in water, any single cylinder i The hydrodynamic force on the surface parallel to the vibration direction of the cylinder is: When multiple cylinders vibrate in water, any single cylinder i The hydrodynamic force on the surface is perpendicular to the vibration direction of the cylinder; and represent any single cylinder in the polycylinder, , is the total number of cylinders in the multi-cylinder array system; represents the attached water mass coefficient parallel to the vibration direction of the multi-cylinder, represents the attached water mass coefficient perpendicular to the vibration direction of the multi-cylinder.

[0025] Further: 、 The expressions are:

[0026] For any two cylinders in the polycylinder 、 The center distance coefficient, ; Any two cylinders in the polyhedron 、 The distance between the centers of the circles; For any two cylinders in the polycylinder 、 The angle between the center line of the circle and the vibration direction, .

[0027] Furthermore, when multiple cylinders vibrate in water, the calculation expression for the attached water mass of any single cylinder is:

[0028] in, When multiple cylinders vibrate in water, any single cylinder i The mass of attached water parallel to the vibration direction, When multiple cylinders vibrate in water, any single cylinder i The mass of attached water perpendicular to the vibration direction.

[0029] The beneficial effects of the present invention are: 1. Based on potential flow theory, the mass of water attached to any single cylinder when multiple cylinders vibrate in water is solved. This method can describe complex fluid dynamics problems using relatively simple mathematical forms, making them easier to understand. In practical engineering applications, the required data can be quickly obtained, improving calculation efficiency, effectively shortening the design cycle, and improving work efficiency.

[0030] 2. The proposed method has broad applicability. It is not only applicable to simple single-column structures but can also effectively handle complex multi-cylinder systems. In multi-cylinder systems, the calculation of attached water mass is typically more complex. However, the proposed method, through clever algorithmic design, accurately accounts for the interactions between individual cylinders, providing accurate and reliable results, which is particularly important in practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Schematic diagram of the process of the present invention; Figure 2 Schematic diagram of the double cylinder structure; Figure 3 This is a comparison diagram of the hydrodynamic time history curves parallel to the vibration direction when the double cylinder vibrates in water; Figure 4 This is a comparison diagram of the hydrodynamic time history curves perpendicular to the vibration direction when the double cylinder vibrates in water; Figure 5 Schematic diagram of pile group foundation of multi-cylinder array system; Figure 6 This is a comparison diagram of the hydrodynamic time history curves parallel to the vibration direction when multiple cylinders vibrate in water; Figure 7 Comparison of the hydrodynamic time history curves perpendicular to the vibration direction when multiple cylinders vibrate in water. DETAILED DESCRIPTION

[0032] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0033] like Figure 1 As shown, the present embodiment provides a method for calculating the attached water mass of a multi-cylinder array system, comprising the following steps: S1. Solve the velocity potential of the flow field when a single cylinder vibrates in water. The specific process is: A single cylinder vibrates horizontally in the form of a simple harmonic wave with an amplitude of , the angular frequency is , the radius of a single cylinder is ; The initial state of water is static, and water is assumed to be an ideal fluid with no viscosity and no rotation.

[0034] Establish a rectangular coordinate system with the center of a single cylinder as the origin ; The rectangular coordinate system Convert to polar coordinates , then the velocity potential of the flow field is expressed as: (1) It represents the velocity potential of the flow field when a single cylinder vibrates in water; is the velocity potential of the flow field when a single cylinder vibrates in water in the polar coordinate system, Satisfies the Laplace equation, which is expressed as: (2) Separate the variables in the above formula and get The calculation formula is: (3) Substituting formula (3) into formula (1), we get The calculation formula is: (4) S2. Solve the velocity potential of the flow field when the double cylinders vibrate in water based on the velocity potential of the flow field when a single cylinder vibrates in water: like Figure 2 As shown, the double cylinder includes a cylinder and cylinder b , with a cylindrical Establish a coordinate system for the origin ; cylinder and cylinder b The spacing between ,cylinder The radius is ,cylinder b The radius is ,cylinder b The polar coordinates of the center of the circle are and cylindrical b The rectangular coordinates of the center of the circle are ;in ; Ignore cylinders With cylinder b The mutual influence of the flow field between the cylinders is calculated according to the solution method of the velocity potential of the flow field when a single cylinder vibrates in water. ,cylinder bVelocity potential of the flow field when vibrating in water: (5) (6) in, For cylinder The velocity potential of the flow field when vibrating in water, For cylinder b Velocity potential of the flow field when vibrating in water; Calculating Cylinders When stationary, the cylinder b Vibrating in water Velocity potential generated at : (7) Represents a cylinder in polar coordinates b Vibrating in water Velocity potential generated at Satisfies the Laplace equation, which is expressed as: (8) Separate the variables in the above formula and get The calculation formula is: (9) in, is a constant whose value is a positive integer. 、 is an intermediate parameter, and its expression is: (10) Substituting equation (9) into equation (7), we get The calculation formula is: (11) Calculate the velocity potential of the flow field when the double cylinders vibrate in water. The velocity potential of the flow field when the double cylinders vibrate in water is Velocity potential when vibrating in water ,cylinder b Velocity potential when vibrating in water and cylindrical Cylinder at rest b Vibrating in water Velocity potential generated at The linear superposition of the cylinder Velocity potential of the surrounding coupled oscillating field , whose expression is: (12).

[0035] S3. Solve the hydrodynamic force on the double cylinders when they vibrate in water based on the velocity potential of the flow field when the double cylinders vibrate in water: Substituting Equation (12) into the linearized Bernoulli equation, we can obtain the hydrodynamic force on the double cylinders when they vibrate in water:

[0036]

[0037] (13)

[0038]

[0039] (14) in, It represents the hydrodynamic force on the surface of any single cylinder parallel to the vibration direction of the cylinder when the double cylinder vibrates in water. It represents the hydrodynamic force on the surface of any single cylinder when the double cylinder vibrates in water in the direction perpendicular to the vibration direction of the cylinder; It represents the hydrodynamic pressure on any single cylinder of the double cylinder in water; represents the attached water mass coefficient parallel to the vibration direction of the double cylinder, represents the attached water mass coefficient perpendicular to the vibration direction of the double cylinder; represents the density of water, represents the mass of water per unit height of a single cylinder, is the acceleration time history of multiple cylinders vibrating in water.

[0040] 、 as well as The calculation expressions are: (15) (16) For cylinder and cylinders b The center distance coefficient between .

[0041] S4. Based on the hydrodynamic forces acting on the two cylinders when vibrating in water, solve the hydrodynamic forces acting on any single cylinder when the multiple cylinders vibrate in water. The hydrodynamic forces acting on any single cylinder when the multiple cylinders vibrate in water are the sum of the hydrodynamic forces acting on the single cylinder by all other cylinders, that is: (17) (18) in, When multiple cylinders vibrate in water, any single cylinder i The hydrodynamic force on the surface parallel to the vibration direction of the cylinder is: When multiple cylinders vibrate in water, any single cylinder i The hydrodynamic force on the surface is perpendicular to the vibration direction of the cylinder; and represent any single cylinder in the polycylinder, , is the total number of cylinders in the multi-cylinder array system; represents the attached water mass coefficient parallel to the vibration direction of the multi-cylinder, represents the attached water mass coefficient perpendicular to the vibration direction of the multi-cylinder.

[0042] 、 The expressions are: (19) For any two cylinders in the polycylinder 、 The center distance coefficient, ; Any two cylinders in the polyhedron 、 The distance between the centers of the circles; For any two cylinders in the polycylinder 、 The angle between the center line of the circle and the vibration direction, .

[0043] S5. Calculate the mass of water attached to any single cylinder based on the hydrodynamic force on the cylinder when the cylinder vibrates in water: (20) in, When multiple cylinders vibrate in water, any single cylinder i The mass of attached water parallel to the vibration direction, When multiple cylinders vibrate in water, any single cylinder i The mass of attached water perpendicular to the vibration direction.

[0044] In order to more clearly illustrate the present invention, the results obtained by the calculation method in the present invention are compared with the solution results of FLUENT numerical simulation software to verify the accuracy and effectiveness of the content of the present invention.

[0045] Verification of working conditions when two cylinders are placed side by side: There are two cylinders C1 and C2, both with a radius of 1.5m, and the center distance coefficient , the angle between the center line of the two cylinders and the vibration direction The cylinder excitation frequency is 1 Hz and the excitation amplitude is 0.3 m. The above data are analyzed using the FLUENT numerical simulation software and the method proposed in this invention, and the hydrodynamic results of the surface of any single cylinder when the double cylinder vibrates in water are compared. Figure 3 、 Figure 4 As shown in the figure, curve C1 represents the hydrodynamic forces acting on cylinder C1 calculated using the method proposed in this invention, while curve C2 represents the hydrodynamic forces acting on cylinder C2 calculated using the method proposed in this invention. Curve An represents the hydrodynamic forces calculated using the FLUENT numerical simulation software. The results show that the hydrodynamic forces calculated using the method proposed in this invention are highly consistent with those obtained using the simulation software.

[0046] Verification of working conditions for multi-cylinder array system: Taking pile group foundation as an example, the calculation accuracy of the hydrodynamic force on any single cylinder when multiple cylinders vibrate in water is verified. Figure 5 As shown, there are 21 cylinders with a radius of 1.5m and a center distance coefficient of 4. The vibration of the pile group foundation uses the actual seismic wave Kocaeli wave, along x Directional excitation. The hydrodynamic forces on cylinder C1 are calculated using the FLUENT numerical simulation software and the method proposed in this invention, and the comparison results are shown in the figure. Figure 6 、 Figure 7 As shown in the figure, curve Fluent-C1 represents the hydrodynamic force on cylinder C1 calculated using the method proposed in this invention, while curve An-C1 represents the hydrodynamic force on cylinder C1 obtained using the FLUENT numerical simulation software. The results show that the calculation results of the proposed method are basically consistent with those obtained by the simulation software, with high accuracy.

[0047] In summary, the calculation results obtained by the method proposed in this invention are not only accurate but also reliable. The simple calculation steps meet the efficiency requirements of actual engineering projects and can significantly improve the quality and efficiency of engineering projects.

Claims

1. A method for calculating attached water mass in a multi-cylinder array system, characterized in that: include: Solve the velocity potential of the flow field when a single cylinder vibrates in water; The velocity potential of the flow field when the double cylinders vibrate in water is solved based on the velocity potential of the flow field when the single cylinder vibrates in water. The hydrodynamic force on the double cylinders when they vibrate in water is solved based on the velocity potential of the flow field when the double cylinders vibrate in water. Based on the hydrodynamic forces on the double cylinders when they vibrate in water, solve the hydrodynamic forces on any single cylinder when multiple cylinders vibrate in water; The attached water mass of any single cylinder is calculated based on the hydrodynamic force on the single cylinder when the multi-cylinder vibrates in water.

2. The method for calculating attached water mass of a multi-cylinder array system according to claim 1, characterized in that: The velocity potential of the flow field when a single cylinder vibrates in water is: in, represents the velocity potential of the flow field when a single cylinder vibrates in water, is the radius of a single cylinder, is the amplitude, is the angular frequency, For time, is the cosine function, is the rectangular coordinate of any point in the flow field, is the polar coordinate of any point in the flow field.

3. The method for calculating attached water mass of a multi-cylinder array system according to claim 2, characterized in that: Double cylinder including cylinder and cylinder b ; When the double cylinder vibrates in water, the velocity potential of the flow field is Velocity potential when vibrating in water ,cylinder b Velocity potential when vibrating in water and cylindrical Cylinder at rest b Vibrating in water Velocity potential generated at The linear superposition of is expressed as: in, is the velocity potential of the flow field when the double cylinders vibrate in water, For cylinder The radius, For cylinder b The radius, For cylinder and cylinder b The spacing between For cylinder b The polar coordinates of the center of the circle, For cylinder b The rectangular coordinates of the center of the circle; is a sine function; 、 is the intermediate parameter, is a constant whose value is a positive integer; For cylinder b Velocity potential of the flow field in polar coordinates when vibrating in water; is the ratio of pi; .

4. The method for calculating attached water mass of a multi-cylinder array system according to claim 3, characterized in that: The hydrodynamic force on the double cylinders when they vibrate in water is: in, It represents the hydrodynamic force on the surface of any single cylinder parallel to the vibration direction of the cylinder when the double cylinder vibrates in water. It represents the hydrodynamic force on the surface of any single cylinder when the double cylinder vibrates in water in the direction perpendicular to the vibration direction of the cylinder; It represents the hydrodynamic pressure on any single cylinder of the double cylinder in water; represents the attached water mass coefficient parallel to the vibration direction of the double cylinder, represents the attached water mass coefficient perpendicular to the vibration direction of the double cylinder; represents the density of water, represents the mass of water per unit height of a single cylinder, is the acceleration time history of multiple cylinders vibrating in water.

5. The method for calculating attached water mass of a multi-cylinder array system according to claim 4, characterized in that: 、 as well as The calculation expressions are: For cylinder and cylinders b The center distance coefficient between .

6. The method for calculating attached water mass of a multi-cylinder array system according to claim 5, characterized in that: When multiple cylinders vibrate in water, the hydrodynamic force on any single cylinder is the sum of the hydrodynamic forces acting on it by all other cylinders. The calculation expression is: in, When multiple cylinders vibrate in water, any single cylinder i The hydrodynamic force on the surface parallel to the vibration direction of the cylinder is: When multiple cylinders vibrate in water, any single cylinder i The hydrodynamic force on the surface is perpendicular to the vibration direction of the cylinder; and represent any single cylinder in the polycylinder, , is the total number of cylinders in the multi-cylinder array system; represents the attached water mass coefficient parallel to the vibration direction of the multi-cylinder, represents the attached water mass coefficient perpendicular to the vibration direction of the multi-cylinder.

7. The method for calculating attached water mass of a multi-cylinder array system according to claim 6, characterized in that: 、 The expressions are: For any two cylinders in the polycylinder 、 The center distance coefficient, ; Any two cylinders in the polyhedron 、 The distance between the centers of the circles; For any two cylinders in the polycylinder 、 The angle between the center line of the circle and the vibration direction, .

8. The method for calculating attached water mass of a multi-cylinder array system according to claim 7, characterized in that: The calculation expression for the mass of water attached to any single cylinder when multiple cylinders vibrate in water is: in, When multiple cylinders vibrate in water, any single cylinder i The mass of attached water parallel to the vibration direction, When multiple cylinders vibrate in water, any single cylinder i The mass of attached water perpendicular to the vibration direction.

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