Method for calculating vortex-induced vibration response of flexible riser based on wake vortex model

Abstract

The application discloses a flexible riser vortex-induced vibration response calculation method based on a wake oscillator model, which is performed according to the following steps: S1, calculating the transverse vibration displacement of the riser according to the structural model of the flexible riser; S2, calculating the wake oscillator variable in the structural model of the flexible riser according to the wake oscillator model; S3, simultaneously solving the structural model of the flexible riser and the wake oscillator model and performing dimensionless processing; S4, performing central difference processing on the equation set after the dimensionless processing; S5, performing iterative calculation on the equation set after the difference processing to obtain the displacement response of the vortex-induced vibration of the flexible riser. The flexible riser vortex-induced vibration response calculation method based on the wake oscillator model can accurately calculate the displacement response of the vortex-induced vibration of the flexible riser under uniform flow and shear flow without identifying parameters from experiments, and can explain the rationality of the flexible riser vortex-induced vibration displacement response calculation method based on the wake oscillator model.

Description

Technical Field

[0001] This invention relates to the field of flexible riser motion monitoring technology, specifically to a method for calculating the vortex-induced vibration response of a flexible riser based on a wake oscillator model. Background Technology

[0002] Although deep-water areas hold abundant oil and gas resources, developing these resources also faces numerous technical problems and challenges. Compared to shallow-water areas, deep-water extraction is more expensive, and many technologies applicable in shallow water are no longer suitable for deep-water extraction. Therefore, the design and operation of deep-sea engineering equipment have become urgent technical issues to be addressed. The floating structure is a key component of deep-sea engineering equipment, comprising the hull and mooring lines. On the one hand, mooring lines prevent excessive displacement of the hull, ensuring smooth operation; on the other hand, they absorb acceleration changes caused by production operations, ensuring safe and reliable production. Therefore, research on flexible risers has received widespread attention.

[0003] Flexible risers in the ocean are affected not only by internal fluid flow but also by external ocean currents. Fluid flowing through the riser creates vortices and causes vortex-induced vibration, which in turn induces fatigue loads and even fatigue failure, significantly reducing the riser's service life. Therefore, research into the mechanism of vortex-induced vibration in flexible risers and accurate response calculations are essential.

[0004] While CFD simulations of vortex-induced vibration in flexible risers can accurately simulate the response, they suffer from long computation times, and in-situ experiments would incur even greater costs. Many wake models exist for vortex-induced vibration, but most require parameter identification from experiments and lack complete physical meaning. Scholar Yukio Tamura proposed a wake model that does not require experimental parameter identification and can accurately calculate the wake oscillator; therefore, it is necessary to propose a model that uses this wake model to accurately predict the displacement response of vortex-induced vibration in flexible risers. Summary of the Invention

[0005] To address the technical problem that existing methods require identifying parameters from experiments to accurately predict the displacement response of vortex-induced vibration of flexible risers, this invention provides a method for calculating the vortex-induced vibration response of flexible risers based on a wake oscillator model.

[0006] The technical solution is as follows:

[0007] A method for calculating the vortex-induced vibration response of a flexible riser based on a wake oscillator model, the key points of which are as follows:

[0008] S1, according to Figure 1The lateral vibration displacement of the flexible riser was calculated using the structural model shown. ;

[0009] S2. Based on the wake oscillator model, calculate the wake oscillator variables in the structural model of the flexible riser. ;

[0010] S3. Combine the structural model of the flexible riser and the wake oscillator model, and perform dimensionless processing to obtain the dimensionless equation set.

[0011] S4. Perform central difference processing on the dimensionless equation system to obtain the differenced equation system.

[0012] S5. Iteratively calculate the equations after differential processing to obtain the displacement response of the vortex-induced vibration of the flexible riser.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0014] The above-mentioned technical solution for calculating the vortex-induced vibration response of flexible risers based on the wake oscillator model can accurately calculate the vortex-induced vibration displacement response of flexible risers under uniform flow and shear flow without identifying parameters from experiments. This explains the rationality of the calculation method for the vortex-induced vibration displacement response of flexible risers based on the wake oscillator model. Attached Figure Description

[0015] Figure 1 This is a structural model of a flexible riser.

[0016] Figure 2 This is a wake oscillator model;

[0017] Figure 3 The graph shows the root mean square displacement distribution along the span of the vortex-induced vibration of the flexible riser when the flow velocity is 0.4 m / s under uniform inflow.

[0018] Figure 4 To obtain the displacement response, take Figure 3 Spectral analysis of the displacement time history at the wave crest yields the frequency-amplitude curve.

[0019] Figure 5 To obtain the displacement response, take Figure 3 Spectral analysis of the displacement time history at the wave crest yields a graph showing the relationship between dimensionless displacement and time.

[0020] Figure 6 This is a graph showing the relationship between fluid velocity and modal number.

[0021] Figure 7 This is a graph showing the relationship between fluid velocity and peak frequency. Detailed Implementation

[0022] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0023] like Figure 1 As shown, a method for calculating the vortex-induced vibration response of a flexible riser based on a wake oscillator model is performed according to the following steps:

[0024] S1. Based on the structural model of the flexible riser, the lateral vibration displacement of the riser is calculated. .

[0025] Specifically, in step S1, the expression for the structural model of the flexible riser is:

[0026] (1)

[0027] In equation (1), Z In the direction of riser span, T For time, For pre-tensioning of risers, EI For the bending stiffness of the riser, M The mass per unit length of the vibrating system. R The damping coefficient is... Lift per unit length;

[0028] Mass per unit length of the vibration system M The expression is:

[0029] (2)

[0030] In equation (2), m s Indicates structural mass. m f Indicates added mass. C M This represents the additional mass coefficient. Since the flexible riser has a cylindrical structure, therefore... C M =1, ρ Indicates fluid density, D Indicates the diameter of the riser pipe;

[0031] Damping coefficient R The expression is:

[0032] (3)

[0033] In equation (3), R s Indicates the structural damping coefficient. R f Indicates the fluid damping coefficient. R f The calculation formula is , γ The stagnation coefficient, γ The calculation formula is , C D The average drag coefficient, S t For the Storoha number, Ω f The vortex shedding circular frequency, Ω f The calculation formula is , U The incoming flow velocity;

[0034] Lift per unit length The expression is:

[0035] (4)

[0036] In equation (4), The lift coefficient, It is calculated by the following formula:

[0037] (5)

[0038] In equation (5), For the wake oscillator variable, f This is the Magnus effect coefficient.

[0039] S2. Based on the wake oscillator model, proposed by scholar Yukio Tamura, this model treats the wake oscillator as a rigid body for calculation, and calculates the wake oscillator variables in the structural model of the flexible riser. .

[0040] Specifically, in step S2, the expression for the wake oscillator model is:

[0041] (6)

[0042] In equation (6), This represents the moment of inertia of the wake oscillator about the center of the cylinder. This represents the damping coefficient of the wake oscillator. Indicates the hydrodynamic restoring moment coefficient. for Figure 2 Half the length of the wake oscillator shown. C L0 This represents the magnitude of the lift coefficient of a stationary cylinder.

[0043] S3. Combine the structural model of the flexible riser and the wake oscillator model, and perform dimensionless processing to obtain the dimensionless equation set.

[0044] Specifically, in step S3, equations (1) and (6) are combined into a system of equations, and dimensionless processing is performed using the following equation (7) to obtain a system of dimensionless equations consisting of the following equations (8) and (9):

[0045] (7)

[0046] In equation (7), This represents the dimensionless lateral vibration displacement of the riser. z For dimensionless span of riser pipe, t For dimensionless time, Ω ref For reference, the circular frequency of vortex shedding, Ω ref The calculation formula is , U ref The incoming flow velocity at the reference height is equal to the uniform incoming flow velocity, i.e.: ;

[0047] (8)

[0048] In equation (8), μ For riser mass ratio, μ The calculation formula is , ω f (z) is the fluid profile coefficient. ω f The formula for calculating (z) is: For uniform flow: For shear flow: , β Indicates the shearing parameter. L The length of the riser is represented by the shear parameter, which allows the vortex-induced vibration displacement response of the flexible riser under shear flow to be calculated using this embodiment. a This is the pretension weighting coefficient. a The calculation formula is , The first-order natural circular frequency, neglecting bending stiffness. f 0 is the first natural frequency of the riser. For speed ratio, The calculation formula is , U cr Indicates the critical flow velocity. b This is the bending stiffness weighting coefficient. b The calculation formula is , The first-order natural circular frequency without considering pretension;

[0049] (9)

[0050] In equation (9), The mass ratio of the wake oscillator. The calculation formula is , L * It is half the length of the dimensionless wake oscillator.

[0051] S4. Perform central difference processing on the dimensionless equation system to obtain the equation system after difference processing.

[0052] Specifically, in step S4, equations (8) and (9) are subjected to central difference processing according to the following equations (10)-(15):

[0053] (10)

[0054] In equation (10), m Representing each spatial point, n Representing each point in time, t n This indicates that time has been divided into grids. z m This indicates that the space has been divided into grids. It represents the lateral displacement of any point in space and at any point in time. Relative to The lateral displacement at the next time point, Relative to The lateral displacement at the previous time point. Indicates the time step;

[0055] (11)

[0056] (12)

[0057] In equation (12), This represents the wake variable at any spatial point and any time point. Relative to The wake variable at the next time point, Relative to The wake variable at the previous time point;

[0058] (13)

[0059] (14)

[0060] In equation (14), Relative to The lateral displacement of the next spatial point, Relative to The lateral displacement of the previous spatial point;

[0061] (15)

[0062] In equation (15), Relative to The lateral displacement of the last two spatial points, Relative to The lateral displacement of the first two spatial points;

[0063] The system of equations obtained by difference processing using the following equations (16) and (17) is as follows:

[0064]

[0065] (16)

[0066]

[0067] (17)

[0068] In equation (16), Indicates the time step. Indicates the spatial step size;

[0069] In equation (17), It is a constant. The expression is , Let be a constant with respect to the Storoch number. The expression is .

[0070] S5. Perform iterative calculations on the equations after differential processing to obtain the displacement response of the vortex-induced vibration of the flexible riser. That is, by using equations (16) and (17) for iterative calculations, the displacement response of the vortex-induced vibration of the flexible riser can be obtained.

[0071] Therefore, without identifying parameters from experiments, the displacement response of vortex-induced vibration of flexible risers under uniform and shear flows can be accurately calculated, which explains the rationality of the calculation method for displacement response of vortex-induced vibration of flexible risers based on the wake oscillator model.

[0072] Please see Figure 1 When the incoming flow passes through the flexible riser, it will cause spatial and temporal changes in the displacement of the flexible riser.

[0073] Please see Figure 2 This wake model assumes that the wake is a Figure 2 The rigid body shown has length and width, and the equation of motion of the wake is established, thereby obtaining the wake oscillator model.

[0074] Figures 3-7 The values ​​are the root mean square value of the vortex-induced vibration displacement, the number of modes, and the peak frequency of the flexible riser, calculated using the vortex-induced vibration response calculation method of this embodiment.

[0075] Specifically, Figure 3 The figure shows the root mean square (RMS) displacement distribution along the span of a flexible riser under uniform inflow velocity of 0.4 m / s. It can be seen from the figure that at a uniform inflow velocity of 0.4 m / s, the vortex-induced vibration displacement of the flexible riser is dominated by the third mode, and the RMS is not zero at the troughs, indicating the existence of a first mode. In other words, the vortex-induced vibration displacement of the flexible riser is the result of the superposition of multiple modes. By changing the inflow velocity, the RMS displacement values ​​at different velocities can be obtained; by changing the flow profile coefficient, the RMS displacement values ​​at different shear layers can be obtained.

[0076] Figure 4 and Figure 5 This indicates that after obtaining the displacement response, for Figure 3 The distribution curve shown is analyzed by taking the displacement time history at the peak of the distribution curve and performing spectral analysis. Figure 4 The frequency-amplitude curve shown in the figure reveals the peak frequency. Comparing this peak frequency with the natural frequencies of the air in the flexible riser in Table 1 shows that the third mode is dominant at this flow velocity, which is consistent with the root mean square (RMS) calculation results. Similarly, results can be obtained by varying the flow velocity.

[0077] Table 1. Calculation results of the natural frequencies of the air riser (unit: Hertz)

[0078] ;

[0079] Figure 6 After obtaining the dominant modes at different flow velocities, it can be seen that: as the flow velocity increases, the dominant mode of vortex-induced vibration displacement in the flexible riser also increases. Figure 6 As can be seen, after the flow velocity is greater than 0.8 m / s, the dominant mode of the riser increases to the 6th mode or above, that is, the higher-order mode is dominant.

[0080] Figure 7 The peak frequencies of vortex-induced vibrations in flexible risers under different flow velocities were summarized, from... Figure 7As can be seen, the peak frequency of vortex-induced vibration of the riser increases with the increase of flow velocity. Similarly, the peak frequency of vortex-induced vibration of the riser can be calculated under uniform flow and shear flow, thus verifying the multi-frequency characteristics of the flexible riser.

[0081] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention. Those skilled in the art, under the guidance of the present invention, can make various similar representations without departing from the spirit and claims of the present invention, and such modifications all fall within the protection scope of the present invention.

Claims

1. A method for calculating the vortex-induced vibration response of a flexible riser based on a wake oscillator model, characterized in that, Follow these steps: S1. Based on the structural model of the flexible riser, the lateral vibration displacement of the riser is calculated. ; S2. Based on the wake oscillator model, calculate the wake oscillator variables in the structural model of the flexible riser. ; S3. Combine the structural model of the flexible riser and the wake oscillator model, and perform dimensionless processing to obtain the dimensionless equation set. S4. Perform central difference processing on the dimensionless equation system to obtain the differenced equation system. S5. Iteratively calculate the equations after differential processing to obtain the displacement response of the vortex-induced vibration of the flexible riser. In step S1, the expression for the structural model of the flexible riser is: （1） In equation (1), Z In the direction of riser span, T For time, For pre-tensioning of risers, EI For the bending stiffness of the riser, M The mass per unit length of the vibrating system. R The damping coefficient is... Lift per unit length; Mass per unit length of the vibration system M The expression is: （2） In equation (2), m s Indicates structural mass. m f Indicates added mass. C M This represents the additional mass coefficient. Since the flexible riser has a cylindrical structure, therefore... C M =1, ρ Indicates fluid density, D Indicates the diameter of the riser pipe; Damping coefficient R The expression is: （3） In equation (3), R s Indicates the structural damping coefficient. R f Indicates the fluid damping coefficient. R f The calculation formula is , γ The stagnation coefficient, γ The calculation formula is , C D The average drag coefficient, S t For the Storoha number, Ω f The vortex shedding circular frequency, Ω f The calculation formula is , U The incoming flow velocity; Lift per unit length The expression is: （4） In equation (4), The lift coefficient, It is calculated by the following formula: （5） In equation (5), For the wake oscillator variable, f The coefficient of the Magnus effect; In step S2, the expression for the wake oscillator model is: （6） In equation (6), This represents the moment of inertia of the wake oscillator about the center of the cylinder. This represents the damping coefficient of the wake oscillator. Indicates the hydrodynamic restoring moment coefficient. This represents half the length of the wake oscillator. C L0 This represents the magnitude of the lift coefficient of a stationary cylinder. In step S3, equations (1) and (6) are combined into a system of equations, and dimensionless processing is performed using the following equation (7) to obtain a system of equations (8) and (9) after dimensionless processing: （7） In equation (7), This represents the dimensionless lateral vibration displacement of the riser. z For dimensionless span of riser pipe, t For dimensionless time, Ω ref For reference, the circular frequency of vortex shedding, Ω ref The calculation formula is , U ref The incoming flow velocity at the reference height is equal to the uniform incoming flow velocity, i.e.: ; （8） In equation (8), μ For riser mass ratio, μ The calculation formula is , ω f (z) is the fluid profile coefficient. ω f The formula for calculating (z) is: For uniform flow: For shear flow: , β Indicates the shearing parameter. L Indicates the length of the riser. a This is the pretension weighting coefficient. a The calculation formula is , The first-order natural circular frequency, neglecting bending stiffness. f 0 is the first natural frequency of the riser. For speed ratio, The calculation formula is , U cr Indicates the critical flow velocity. b This is the bending stiffness weighting coefficient. b The calculation formula is , The first-order natural circular frequency without considering pretension; （9） In equation (9), The mass ratio of the wake oscillator. The calculation formula is , L * It is half the length of the dimensionless wake oscillator.

2. The method for calculating the vortex-induced vibration response of a flexible riser based on a wake oscillator model according to claim 1, characterized in that, In step S4, equations (8) and (9) are subjected to central difference processing according to the following equations (10)-(15): （10） In equation (10), m Representing each spatial point, n Representing each point in time, t n This indicates that time has been divided into grids. z m This indicates that the space has been divided into grids. It represents the lateral displacement of any point in space and at any point in time. Relative to The lateral displacement at the next time point, Relative to The lateral displacement at the previous time point. Indicates the time step; （11） （12） In equation (12), This represents the wake variable at any spatial point and any time point. Relative to The wake variable at the next time point, Relative to The wake variable at the previous time point; （13） （14） In equation (14), Relative to The lateral displacement of the next spatial point, Relative to Lateral displacement of the previous spatial point （15） In equation (15), Relative to The lateral displacement of the last two spatial points, Relative to The lateral displacement of the first two spatial points; The system of equations obtained by difference processing using the following equations (16) and (17) is as follows: (16) （17） In equation (16), Indicates the time step. Indicates the spatial step size; In equation (17), It is a constant. The expression is , Let be a constant with respect to the Storoch number. The expression is .

3. The method for calculating the vortex-induced vibration response of a flexible riser based on a wake oscillator model according to claim 2, characterized in that, In step S5, the displacement response of the vortex-induced vibration of the flexible riser is obtained by iterative calculation using equations (16) and (17).

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