A Tuned Liquid Three-column Star Damper for Wind Turbine Towers

Abstract

The present invention discloses a tuned liquid three-column star damper for a wind power tower, which comprises a three-way prism water tank, an L-shaped pipe and a connecting air pipe; the bottom of the three-way prism water tank is flexibly connected to an additional platform of the wind power tower through a spring, and each of the three spaced side surfaces of the three-way prism water tank is provided with an opening flange for outputting liquid, the opening flange is connected to the short side of the L-shaped pipe, the L-shaped pipe is internally provided with an opening damping baffle, and by adjusting the opening area of the opening damping baffle, the adjustment of the damping ratio is realized, the long side of the L-shaped pipe is connected to a ventilation hole of the yaw platform of the wind power tower, and the connecting air pipe connects the respective ventilation holes of the yaw platform of the wind power tower, so as to seal the gas and liquid in the L-shaped pipe, and the frequency modulation of the damper can be realized by increasing or decreasing the liquid; the present invention realizes the functions of low-frequency vibration control and multi-dimensional vibration control, and has a simple design structure, is applicable to the internal space of the wind power tower, and meets the requirements of vibration control of wind turbine units.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration control of wind turbines, and particularly to a tuned liquid three-column star damper for a wind power tower. Background Art

[0002] The natural vibration frequency of an ultra-high wind power tower is low, and the airflow around it is likely to induce some abnormal vibrations. The offshore wind power tower is under the combined action of wind and waves, and the lateral vibration is relatively large. It is very difficult for a wind turbine to completely avoid these abnormal vibrations through its own electrical control, and power generation loss will inevitably occur during the electrical control process. Therefore, equipping a damper for vibration control is an effective solution. Among them, dampers can be divided into two categories: tuned mass dampers and tuned liquid dampers. The oscillator of a tuned mass damper is a solid such as a steel block, and the effect is relatively large, but it requires special energy-consuming devices and limit devices, with a complex structure and high cost. The oscillator of a tuned liquid damper is a liquid such as water, which can utilize the viscous flow or flow around obstacles of the liquid itself to consume energy. The device structure is simple, without safety risks such as collision, and the cost is relatively low.

[0003] However, in the wind power generation industry, the space on the wind power tower is limited, and the natural vibration frequency of the structure is low, which has certain limitations on the application of dampers. Therefore, the application of dampers is still in the development and test stage. Currently, the tuned mass dampers applied to wind turbines include types such as pendulums and guide rail sliders, and the tuned liquid dampers include forms such as TLD and TLCD. Limited by the structural space, the diameter of the TLD damper is small, and the tuning frequency is relatively high, which is only suitable for the second-order vibration control of the wind power tower. The traditional TLCD damper has a single control direction and is not suitable for wind turbines with variable load directions.

[0004] Therefore, to solve the above technical problems, it is necessary to provide a damper with multi-dimensional vibration control, low cost, good effect, simple structure, and low control frequency to overcome the defects in the prior art. Summary of the Invention

[0005] The purpose of the present invention is to provide a tuned liquid three-column star damper for a wind power tower to solve the deficiencies in the prior art, realizing the functions of low-frequency vibration control and multi-dimensional vibration control, with a simple design structure, suitable for the internal space of the wind power tower, and meeting the requirements of wind turbine vibration control.

[0006] To achieve the above object, the technical solution provided by the present invention is: a tuned liquid three-column star damper for a wind turbine tower. The damper includes a three-way prism water tank, three L-shaped pipes, and a connecting air pipe; three spaced side surfaces of the three-way prism water tank are respectively provided with opening flanges for outputting liquid, each opening flange corresponds to an L-shaped pipe, the opening flange is connected to the short side of the L-shaped pipe, and the L-shaped pipe is internally provided with an opening damping baffle. By adjusting the opening area of the opening damping baffle, local pressure drop loss is generated in the liquid in the L-shaped pipe, so as to realize the adjustment of the damping ratio. The long side of the L-shaped pipe is connected to the vent hole of the yaw platform of the wind turbine tower, and a connecting air pipe is installed on the yaw platform of the wind turbine tower, and the connecting air pipe communicates with each vent hole of the yaw platform of the wind turbine tower, so as to seal the gas and liquid in the L-shaped pipe. By increasing or decreasing the liquid, the frequency modulation of the damper can be realized. The bottom of the three-way prism water tank is flexibly connected to the additional platform of the wind turbine tower through a spring, and the additional platform of the wind turbine tower shares part of the vertical load of the damper, and at the same time inhibits the deformation of the L-shaped pipe under the action of gravity.

[0007] Further, it further includes a plurality of flexible connection components. The flexible connection components include a first connection head, a second connection head, a connecting plate, a high-elastic non-metallic gasket, and a bolt assembly. The first connection head is welded to the outer wall of the L-shaped pipe, the second connection head is welded to the inner wall of the wind turbine tower, the first connection head and the second connection head are connected through a connecting plate, and are pre-tightened by a bolt assembly. The high-elastic non-metallic gasket is clamped between the first connection head and the connecting plate. The high-elastic non-metallic gasket can prevent the deformation constraint force of the wind turbine tower from being transmitted within the flexible connection components, avoiding over-constraint internal forces, and at the same time enabling the horizontal control force of the damper to be transmitted to the inner wall of the wind turbine tower, thereby controlling the vibration of the wind turbine tower.

[0008] Further, it further includes a plurality of bracket supports. The bracket supports include an open rectangular frame, a first diagonal brace, and a second diagonal brace. The open rectangular frame is sleeved outside the L-shaped pipe and is located below the second vertical pipe of the L-shaped pipe and the upper flange of the reversing elbow. The two open ends of it are connected to the inner wall of the wind turbine tower. One end of the first diagonal brace is respectively connected to the inner wall of the wind turbine tower and a right angle of the open rectangular frame, and one end of the second diagonal brace is respectively connected to the inner wall of the wind turbine tower and the other right angle of the open rectangular frame. The bracket support is flexibly connected to the second vertical pipe of the L-shaped pipe and the upper flange of the reversing elbow through a spring, providing a supporting force for the L-shaped pipe, and at the same time distributing the vertical load of the L-shaped pipe to the inner wall of the wind turbine tower, avoiding the concentrated distribution of the vertical force of the damper.

[0009] Further, the L-shaped pipe includes a first vertical pipe, a second vertical pipe, and a reversing elbow. Upper and lower flanges are configured at both ports of the first vertical pipe, the second vertical pipe, and the reversing elbow. The upper flange of the first vertical pipe is connected to the ventilation hole of the yaw platform of the wind turbine tower through bolts. The lower flange of the first vertical pipe is connected to the upper flange of the second vertical pipe. The lower flange of the second vertical pipe is connected to the upper flange of the reversing elbow. An inner sunk platform for installing an opening damping baffle is provided on the upper flange of the reversing elbow, which can clamp the outer edge of the opening damping baffle between the lower flange of the second vertical pipe and the upper flange of the reversing elbow. The lower flange of the reversing elbow is connected to the opening flange of the three-way prism water tank.

[0010] Further, the connecting air pipe includes a three-way joint, a first elbow joint, a second elbow joint, an annular round anchor plate, and an arc pipe. Annular round anchor plates are provided at the flange ends of the three-way joint, the first elbow joint, and the second elbow joint. The annular round anchor plate of the three-way joint is fixed to one of the ventilation holes of the yaw platform of the wind turbine tower through bolts. The annular round anchor plates of the first elbow joint and the second elbow joint are respectively fixed to the other two ventilation holes of the yaw platform of the wind turbine tower through bolts. Arc pipes are connected between the ports of the first elbow joint and the three-way joint and between the ports of the second elbow joint and the three-way joint.

[0011] Further, the opening damping baffle is an opening thin plate or a wire rope net.

[0012] Further, the three-way prism water tank is a hexagonal prism water tank. A hollow cable through-hole is formed in the middle part of the three-way prism water tank. The distances between the three opening flanges of the three-way prism water tank are equal.

[0013] Further, the upper flanges of the second vertical pipe and the reversing elbow are both three-petal flanges.

[0014] Further, the mathematical expression for the vibration control of the damper is the following differential equation:

[0015]

[0016] where M is the mass matrix of the wind turbine tower, C is the damping matrix of the wind turbine tower, K is the stiffness matrix of the wind turbine tower, and F is the external load matrix of the wind turbine tower;

[0017] X is the displacement matrix of the wind turbine tower body, is the velocity matrix of the wind turbine tower body, is the acceleration matrix of the wind turbine tower body;

[0018] is the point acceleration at the installation position of the wind turbine tower body damper;

[0019] W is the liquid level displacement, is the liquid level velocity, is the liquid surface acceleration;

[0020] H=[0…0 1 0…0] T , where element 1 represents that a damper is provided at the corresponding position of the tower body. If there are multiple elements 1, it means that multiple dampers are arranged on the tower body;

[0021] ρ is the liquid density, A is the cross-sectional area of ​​the liquid column, h is the height of the liquid level at rest, and r is the length of the horizontal liquid column in the L-shaped pipe;

[0022] g is the acceleration due to gravity;

[0023] ξ is the nonlinear damping coefficient, including the damping coefficient generated by the damping baffle.

[0024] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0025] 1. This damper can achieve frequency modulation by adding or reducing liquid, the frequency can be set very low, and multi-dimensional vibration control can be achieved at the same time, which is suitable for the needs of wind turbine vibration control.

[0026] 2. The structure of the damper is simple, and its energy dissipation device is only a perforated damping baffle. The damping ratio can be adjusted by adjusting the opening area of ​​the baffle, and it has a wide damping ratio adjustment capability.

[0027] 3. The damper is flexibly connected to the wind tower through a spring to disperse the load, avoid concentrated load distribution, and increase the safety of the connection; at the same time, the flexible connection component is built with a highly elastic non-metallic gasket to reduce the constraint stress of the wind load deformation of the wind tower on the first connector and the second connector, thereby increasing the safety of the connection. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Schematic diagram of the structure of a tuned liquid three-column star damper.

[0029] Figure 2 It is a structural schematic diagram of a three-way prismatic water tank.

[0030] Figure 3 This is a schematic diagram of the structure of an L-shaped pipeline.

[0031] Figure 4 Schematic diagram of the structure of the perforated damping baffle.

[0032] Figure 5 It is a structural schematic diagram of the corbel support frame.

[0033] Figure 6 It is a structural schematic diagram of the flexible connection component. DETAILED DESCRIPTION

[0034] The present invention will be further described below in conjunction with specific embodiments.

[0035] See Figures 1 to 6 As shown, this embodiment provides a tuned liquid three-column star damper for a wind turbine tower, including a tee-prism water tank 1, three L-shaped pipes 2, a connecting air pipe 3, a flexible connection assembly 4, and a bracket support 5;

[0036] Among them, the tee-prism water tank 1 is a hexagonal prism water tank. A hollow cable through-hole 1-2 is formed in the middle part of the tee-prism water tank 1. Three spaced side surfaces of the tee-prism water tank 1 are respectively provided with opening flanges 1-1 for outputting liquid, and the three opening flanges 1-1 are equidistant. The opening flange 1-1 is connected to the short side of the L-shaped pipe 2. The L-shaped pipe 2 is internally provided with an opening damping baffle 8. The opening damping baffle 8 is an opening thin plate. By adjusting the opening area of the opening damping baffle 8, local pressure drop loss is generated in the liquid in the L-shaped pipe 2, so as to realize the adjustment of the damping ratio. The long side of the L-shaped pipe 2 is connected to the vent hole of the yaw platform 7 of the wind turbine tower. A connecting air pipe 3 is installed on the yaw platform 7 of the wind turbine tower. The connecting air pipe 3, the long side of the L-shaped pipe 2, and the yaw platform 7 of the wind turbine tower are fastened by bolts to connect the connecting air pipe 3 to each vent hole of the yaw platform 7 of the wind turbine tower, so as to seal the gas and liquid in the L-shaped pipe 2. The frequency of the damper can be adjusted by increasing or decreasing the liquid. A plurality of spring positioning rings are provided at the bottom of the tee-prism water tank 1, and a spring 1-3 is sleeved thereon. It is flexibly connected to the additional platform 6 of the wind turbine tower through the spring 1-3. The additional platform 6 of the wind turbine tower shares part of the vertical load of the damper and simultaneously inhibits the deformation of the L-shaped pipe 2 under the action of gravity.

[0037] The L-shaped pipe 2 includes a first vertical pipe 2-1, a second vertical pipe 2-2, and a reversing elbow 2-3. Upper and lower flanges are configured at both ports of the first vertical pipe 2-1, the second vertical pipe 2-2, and the reversing elbow 2-3. The upper flanges of the second vertical pipe 2-2 and the reversing elbow 2-3 are both three-petal flanges. The upper flange of the first vertical pipe 2-1 is connected to the vent hole of the yaw platform 7 of the wind turbine tower by bolts. The lower flange of the first vertical pipe 2-1 is connected to the upper flange of the second vertical pipe 2-2. The lower flange of the second vertical pipe 2-2 is connected to the upper flange of the reversing elbow 2-3. An inner sink is provided on the upper flange 2-3-1 of the reversing elbow for installing the opening damping baffle 8, which can clamp the outer edge of the opening damping baffle 8 between the lower flange of the second vertical pipe 2-2 and the upper flange of the reversing elbow 2-3. The lower flange of the reversing elbow 2-3 is connected to the opening flange 1-1 of the tee-prism water tank 1.

[0038] The connecting air pipe 3 includes a three-way joint 3-1, a first elbow joint 3-2, a second elbow joint 3-3, an annular circular anchor plate 3-4 and an arc pipe 3-5. The flange ends of the three-way joint 3-1, the first elbow joint 3-2 and the second elbow joint 3-3 are all equipped with annular circular anchor plates 3-4. The annular circular anchor plate 3-4 of the three-way joint 3-1 is fixed on one of the ventilation holes of the yaw platform 7 of the wind turbine tower by bolts. The annular circular anchor plates 3-4 of the first elbow joint 3-2 and the second elbow joint are respectively fixed on the other two ventilation holes of the yaw platform 7 of the wind turbine tower by bolts. Arc pipes 3-5 are connected between the ports of the first elbow joint 3-2 and the three-way joint 3-1, and between the ports of the second elbow joint 3-3 and the three-way joint 3-1.

[0039] The flexible connection assembly 4 is close to the lower flanges of the first vertical pipe 2-1 and the second vertical pipe 2-2. It includes a first connector 4-1, a second connector 4-2, a connecting plate 4-3, a highly elastic non-metallic gasket 4-4 and a bolt assembly. The first connector 4-1 is welded to the outer wall of the L-shaped pipe 2. The second connector 4-2 is welded to the inner wall of the wind turbine tower. The first connector 4-1 and the second connector 4-2 are connected by the connecting plate 4-3 and pre-tightened with the bolt assembly. The highly elastic non-metallic gasket 4-4 is clamped between the first connector 4-1 and the connecting plate 4-3. This highly elastic non-metallic gasket 4-4 can prevent the deformation restraint force of the wind turbine tower from being transmitted within the flexible connection assembly 4, avoiding over-constraint internal forces. At the same time, it also enables the horizontal control force of the damper to be transmitted to the inner wall of the wind turbine tower, thereby controlling the vibration of the wind turbine tower.

[0040] The corbel support 5 includes an open rectangular frame 5-1, a first diagonal brace 5-2 and a second diagonal brace 5-3. End plates are welded to the ends of the corbel support 5 and fixed to the inner wall of the wind turbine tower by internal thread posts and hexagon flange bolts welded to the inner wall of the wind turbine tower. The open rectangular frame 5-1 is sleeved outside the L-shaped pipe 2 and is located below the second vertical pipe of the L-shaped pipe 2 and the upper flange of the reversing elbow. Its open ends are fixed to the inner wall of the wind turbine tower. One end of the first diagonal brace 5-2 is welded to a right angle of the open rectangular frame 5-1, and its other end is fixed to the inner wall of the wind turbine tower. One end of the second diagonal brace 5-3 is welded to the other right angle of the open rectangular frame 5-2, and its other end is fixed to the inner wall of the wind turbine tower by bolts. The corbel support 5 is flexibly connected to the upper flanges of the second vertical pipe 2-2 and the reversing elbow 2-3 through springs 5-4, providing a support force for the L-shaped pipe 2 and at the same time distributing the vertical load of the L-shaped pipe 2 to the inner wall of the wind turbine tower, avoiding the concentrated distribution of the vertical force of the damper.

[0041] The mathematical expression for the vibration control of the above damper can be the following differential equation:

[0042]

[0043] Among them, M is the mass matrix of the wind power tower, C is the damping matrix of the wind power tower, K is the stiffness matrix of the wind power tower, and Ft is the external load matrix of the wind power tower;

[0044] X is the displacement matrix of the wind power tower body, is the velocity matrix of the wind power tower body, is the acceleration matrix of the wind power tower body;

[0045] is the point acceleration at the installation position of the damper on the wind power tower body;

[0046] W is the liquid level displacement, is the liquid level velocity, is the liquid level acceleration;

[0047] H = [0…0 1 0…0] T , where the element 1 represents that there is a damper at the corresponding position of the tower body. If there are multiple elements 1, it means that there are multiple dampers arranged on the tower body;

[0048] ρ is the liquid density, A is the cross-sectional area of the liquid column, h is the liquid level height at rest, and r is the length of the horizontal liquid column of the L-shaped pipe 2;

[0049] g is the acceleration due to gravity;

[0050] ξ is the non-linear damping coefficient, including the damping coefficient generated by the damping baffle.

[0051] The above-described embodiments are only the preferred embodiments of the present invention, and do not limit the scope of implementation of the present invention. Therefore, all changes made according to the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A tuned liquid three-column star damper for a wind power tower, characterized in that: The damper includes a three-way prism water tank (1), three L-shaped pipes (2) and a connecting air pipe (3); openings flanges (1-1) for outputting liquid are respectively arranged on three spaced side surfaces of the three-way prism water tank (1), each openings flange (1-1) corresponds to an L-shaped pipe (2), the openings flange (1-1) is connected to the short side of the L-shaped pipe (2), an opening damping baffle (8) is arranged inside the L-shaped pipe (2), by adjusting the opening area of the opening damping baffle (8), local pressure drop loss of the liquid in the L-shaped pipe (2) is generated, so as to realize the adjustment of the damping ratio, the long side of the L-shaped pipe (2) is connected to the ventilation hole of the yaw platform (7) of the wind turbine tower, the connecting air pipe (3) is installed on the yaw platform (7) of the wind turbine tower, and the connecting air pipe (3) communicates with each ventilation hole of the yaw platform (7) of the wind turbine tower, so as to seal the gas and liquid in the L-shaped pipe (2), and the frequency modulation of the damper can be realized by increasing or decreasing the liquid. The bottom of the three-way prism water tank (1) is flexibly connected to the additional platform (6) of the wind turbine tower through a spring, and the additional platform (6) of the wind turbine tower shares part of the vertical load of the damper and simultaneously inhibits the deformation of the L-shaped pipe (2) under the action of gravity.

2. The tuned liquid three-column star damper for a wind power tower according to claim 1, characterized in that: It further includes a plurality of flexible connection components (4), the flexible connection components (4) include a first connection head (4-1), a second connection head (4-2), a connecting plate (4-3), a high-elastic non-metallic gasket (4-4) and a bolt assembly. The first connection head (4-1) is welded on the outer wall of the L-shaped pipe (2), the second connection head (4-2) is welded on the inner wall of the wind turbine tower, the first connection head (4-1) and the second connection head (4-2) are connected through the connecting plate (4-3) and pre-tightened by the bolt assembly, and the high-elastic non-metallic gasket (4-4) is clamped between the first connection head (4-1) and the connecting plate (4-3). The high-elastic non-metallic gasket (4-4) can prevent the deformation constraint force of the wind turbine tower from being transmitted inside the flexible connection component (4) to avoid over-constraint internal force, and at the same time, the horizontal control force of the damper is transmitted to the inner wall of the wind turbine tower, so as to control the vibration of the wind turbine tower.

3. The tuned liquid three-column star damper for a wind power tower according to claim 1, characterized in that: It further includes a plurality of bracket supports (5), and each bracket support (5) includes an open rectangular frame (5-1), a first diagonal brace (5-2) and a second diagonal brace (5-3). The open rectangular frame (5-1) is sleeved outside the L-shaped pipe (2) and is located below the second vertical pipe (2-2) of the L-shaped pipe (2) and the upper flange of the reversing elbow (2-3). The two open ends thereof are connected to the inner wall of the wind turbine tower. One end of the first diagonal brace (5-2) is respectively connected to the inner wall of the wind turbine tower and a right angle of the open rectangular frame (5-1), and one end of the second diagonal brace (5-3) is respectively connected to the inner wall of the wind turbine tower and the other right angle of the open rectangular frame (5-1). The bracket support (5) is flexibly connected to the second vertical pipe (2-2) of the L-shaped pipe (2) and the upper flange of the reversing elbow (2-3) through a spring, providing a supporting force for the L-shaped pipe (2), and at the same time distributing the vertical load of the L-shaped pipe (2) to the inner wall of the wind turbine tower to avoid the concentrated distribution of the vertical force of the damper.

4. The tuned liquid three-column star damper for a wind power tower according to claim 1, characterized in that: The L-shaped pipe (2) includes a first vertical pipe (2-1), a second vertical pipe (2-2) and a reversing elbow (2-3). Upper and lower flanges are configured at both ports of the first vertical pipe (2-1), the second vertical pipe (2-2) and the reversing elbow (2-3). The upper flange of the first vertical pipe (2-1) is connected to the ventilation hole of the yaw platform (7) of the wind turbine tower through bolts. The lower flange of the first vertical pipe (2-1) is connected to the upper flange of the second vertical pipe (2-2). The lower flange of the second vertical pipe (2-2) is connected to the upper flange of the reversing elbow (2-3). An inner sunk platform for installing an open-hole damping baffle (8) is provided on the upper flange (2-3-1) of the reversing elbow, so that the outer edge of the open-hole damping baffle (8) can be clamped between the lower flange of the second vertical pipe (2-2) and the upper flange of the reversing elbow (2-3). The lower flange of the reversing elbow (2-3) is connected to the opening flange (1-1) of the three-way prism water tank (1).

5. The tuned liquid three-column star damper for a wind power tower according to claim 1, characterized in that: The connecting air pipe (3) includes a three-way joint (3-1), a first elbow joint (3-2), a second elbow joint (3-3), an annular round anchor plate (3-4) and an arc pipe (3-5). Annular round anchor plates (3-4) are provided at the flange ends of the three-way joint (3-1), the first elbow joint (3-2) and the second elbow joint (3-3). The annular round anchor plate (3-4) of the three-way joint (3-1) is fixed to one of the ventilation holes of the yaw platform (7) of the wind turbine tower through bolts. The annular round anchor plates (3-4) of the first elbow joint (3-2) and the second elbow joint (3-3) are respectively fixed to the other two ventilation holes of the yaw platform (7) of the wind turbine tower through bolts. Arc pipes (3-5) are connected between the ports of the first elbow joint (3-2) and the three-way joint (3-1) and between the ports of the second elbow joint (3-3) and the three-way joint (3-1).

6. The tuned liquid three-column star damper for a wind power tower according to claim 1, characterized in that: The open-hole damping baffle (8) is an open-hole thin plate or a wire rope net.

7. The tuned liquid three-column star damper for a wind power tower according to claim 1, characterized in that: The three-way prism water tank (1) is a hexagonal prism water tank. A hollow cable through-hole (1-2) is formed in the middle of the three-way prism water tank (1), and the distances between the three opening flanges (1-1) of the three-way prism water tank (1) are equal.

8. The tuned liquid three-column star damper for a wind power tower according to claim 4, characterized in that: The upper flanges of the second vertical pipe (2-2) and the reversing elbow (2-3) are both three-petal flanges.

9. The tuned liquid three-column star damper for a wind power tower according to claim 1, characterized in that: The mathematical expression for the vibration control of the damper is the following differential equation: where M is the mass matrix of the wind turbine tower, C is the damping matrix of the wind turbine tower, K is the stiffness matrix of the wind turbine tower, and F(t) is the external load matrix of the wind turbine tower; X is the displacement matrix of the wind turbine tower body, is the velocity matrix of the wind turbine tower body, is the acceleration matrix of the wind turbine tower body; is the point acceleration at the installation position of the wind turbine tower damper; W is the liquid level displacement, is the liquid level velocity, is the liquid level acceleration; H = [0…0 1 0…0] T , where the element 1 indicates that a damper is provided at the corresponding position of the tower body, and if there are multiple elements 1, it means that multiple dampers are arranged on the tower body; ρ is the liquid density, A is the cross-sectional area of the liquid column, h is the liquid level height at rest, and r is the length of the horizontal liquid column of the L-shaped pipe (2); g is the acceleration due to gravity; ξ is the non-linear damping coefficient, including the damping coefficient generated by the damping baffle.

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