A method for calculating coupled vibration of rotating cylindrical flow-induced vibration and inertial vortex vibration

Abstract

The application relates to a kind of rotating cylindrical flow-induced vibration and inertial vortex coupling vibration calculation methods, S1, establishes two-dimensional numerical model;S2, numerical model is divided into region and grid;S3, UDF secondary development program is compiled;S4, set fluid parameter, boundary condition and solution parameter;S5, solve flow field model, obtain the load of cylindrical surface;S6, the force suffered by structure is calculated through UDF, the result is brought into the differential dynamics equation of cylindrical eccentric vibration system;the vibration response program of structure based on four-order Runge-Kutta method is called to solve the equation, and the displacement, velocity, acceleration of structure are obtained;S7, the displacement, velocity, acceleration of structure are passed to cylinder, and the angular velocity of cylinder rotation is defined through UDF;S8, the calculation result of cylinder is output;S9, whether the current cylinder vibration is stable is judged, if yes, end calculation;otherwise, solve the flow field of next time step, repeat steps S5-S9.The application can accurately reflect the vortex-induced vibration response condition of eccentric rotating cylinder.

Description

Technical Field

[0001] This invention relates to the field of marine engineering technology, specifically to a method for calculating the coupled vibration of a rotating cylinder caused by flow and inertial eddy currents. Background Technology

[0002] Marine riser systems are crucial structures in marine engineering, undertaking vital functions such as oil and gas transportation. When ocean currents pass over marine risers, alternating vortex shedding occurs, causing periodic vibrations in the riser structure, known as vortex-induced vibration (VIV). During the response of VIV, the surface excitation force generated by vortex shedding triggers structural vibration, which in turn affects the fluid vortex shedding, thus influencing the excitation force. This is a typical nonlinear fluid-structure interaction problem.

[0003] Drill strings are used in marine energy exploration, including oil, natural gas, and minerals. The operation is a complex technical task involving significant costs and risks. In drilling systems, drill bit vibration, high pressure, and high frictional resistance can easily lead to stick-slip, rotation, and lateral vibration of the drill string, increasing the risk of drilling accidents. Lateral displacement of the drill string causes the structural center to separate from the rotation center, generating eccentric forces that affect the drill string's vibration. Since the eccentric force fluctuates at the drill string's rotational frequency, there is often an eccentric component at that frequency in the drill string's vibration. Besides the eccentrically induced vibration (vibration caused by the eccentric force generated by the eccentrically rotating cylinder) generated by the drill string in the borehole, components at the rotational frequency of rotating cylinders in flow have also been observed. Current research on the vibration of rotating cylinders in flow mainly simplifies eccentrically induced vibration, considering only the influence of fluid forces on the vibration. Further research is needed on the coupled vibration problem of flow-induced vibration (FIV) and eccentricity-induced vibration (EIV) of rotating cylinders in flow. Summary of the Invention

[0004] The technical problem to be solved by this invention is to address the shortcomings of the existing technology in the study of the vibration of a rotating cylinder in flow, which simplifies the eccentric-induced vibration and only considers the influence of fluid force on the vibration. This invention provides a method for calculating the coupled vibration of a rotating cylinder with flow-induced vibration and inertial eddy current. This method considers the influence of cylinder eccentricity, constructs a coupled vibration model of a rotating cylinder with FIV and EIV based on FIV and EIV, analyzes the coupling response characteristics of FIV and EIV of the rotating cylinder, solves the flow field based on Fluent software, and performs secondary development of Fluent functions by compiling UDF programs to realize the numerical simulation of the coupled vibration of a rotating cylinder with flow-induced vibration and inertial eddy current (i.e., eccentric-induced vibration).

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] A method for calculating the coupled vibration of a rotating cylinder caused by flow and inertial eddy currents includes the following steps:

[0007] S1. Establish a two-dimensional numerical model of the coupled vibration of the rotating cylinder caused by flow and inertial eddy current.

[0008] S2. Divide the numerical model into regions. The flow field from the cylindrical surface to the boundary is divided into a rigid region, a dynamic mesh region, and a static mesh region. Determine the mesh size and perform mesh generation. Generate a mesh file and import it into Fluent software.

[0009] S3. To realize the structural fluid-structure interaction calculation in Fluent software, compile a UDF secondary development program; set the cylinder dynamic parameters in the UDF secondary development program, and embed the UDF secondary development program into Fluent software;

[0010] S4. Set the fluid parameters, boundary conditions, and solution parameters in Fluent software;

[0011] S5. Solve the flow field model using Fluent software. The flow field calculation is performed by discretizing the Reynolds-averaged incompressible Navier-Stokes equations using the finite volume method, thereby obtaining the flow field characteristics in the model and acquiring the load on the cylindrical surface.

[0012] S6. Based on the obtained cylindrical surface load, the forces on the structure composed of the cylinder and the spring damping system are calculated by UDF. The results are then substituted into the differential dynamic equation of the cylindrical eccentric vibration system. The structural vibration response program based on the fourth-order Runge-Kutta method is called to solve the differential dynamic equation of the cylindrical eccentric vibration system to obtain the displacement, velocity, and acceleration of the structure.

[0013] S7. The displacement, velocity, and acceleration of the structure are transmitted to the cylinder through UDF to realize the displacement of the cylinder; the rotational angular velocity of the cylinder is defined through UDF to realize the rotation of the cylinder; the movement of the mesh boundary and the updating of the mesh are realized through the dynamic mesh model.

[0014] S8. Output the calculation results of the cylinder, including transverse displacement, downstream displacement, lift and drag, through UDF and Fluent.

[0015] S9. Determine whether the current cylindrical vibration is stable based on the output results. If it is, end the calculation; otherwise, solve the flow field for the next time step and repeat steps S5 to S9.

[0016] In the above scheme, in steps S1 and S2, ICEM CFD software is used for model building and mesh generation; a triangular mesh is used globally, and a boundary layer mesh is set on the cylindrical wall; the rigid region is the cylindrical wall and part of the boundary layer region, the dynamic mesh region is the region near the cylinder, and the other regions of the flow field are static mesh regions.

[0017] In the above scheme, the set cylinder dynamic parameters in step S3 include diameter, density, natural frequency, and damping coefficient.

[0018] In the above scheme, in step S4, the boundary conditions are: the left boundary condition is the velocity inlet; the right boundary condition is the pressure outlet; the upper and lower boundary conditions are symmetrical boundaries; and the cylindrical surface is a non-slip wall surface.

[0019] In the above scheme, step S4 includes setting the solution parameters, including: turbulence model, solution algorithm, discretization scheme, solution accuracy, and time step.

[0020] In the above scheme, in step S6, the differential dynamic equation of the cylindrical eccentric vibration system is a differential dynamic equation considering the coupling effect of eccentric force and fluid force, wherein:

[0021] The governing equations of the cylindrical eccentric vibration system are:

[0022]

[0023] The cylinder is supported by a spring-damped system, which includes a transverse linear elastic spring K1 and a co-current linear elastic spring K2, as well as a transverse damping system C1 and a co-current damping system C2. k represents the elastic coefficient of the spring-damped system, and c represents the damping coefficient. m is the mass of the cylinder, t represents time, and y(t) is the unit of measurement. Let x(t) represent the dimensionless displacement, velocity, and acceleration of the cylinder in the transverse direction. Let represent the dimensionless displacement, velocity, and acceleration of the cylinder in the downstream direction, respectively.

[0024] F e1 and F e2 These are the eccentric forces in the cross-flow direction and the downstream direction, respectively. Their magnitudes depend on the eccentric distance E, the rotational speed Ω, and the mass m of the cylinder, while their directions depend on the rotation angle.

[0025]

[0026] The governing equation for the flow-induced vibration of a cylinder is:

[0027]

[0028] Where, m * =4m / (ρπD)2 () represents the mass ratio of the cylinder. Represents the damping ratio, C d C represents the flow coefficient on the cylindrical surface. d =2F x / ρDU 2 C l C represents the crossflow force coefficient on the cylindrical surface. l =2F y / ρDU 2 F x F y Let ρ represent the fluid forces acting on the cylinder in the downstream and cross-current directions, respectively; let D represent the cylinder density; let U represent the cylinder diameter; and let V represent the downstream fluid velocity. r The reduction rate is represented by V. r =U / (f n ×D), The natural frequency of the cylinder;

[0029] Adding equations (1) and (3) together yields the differential dynamic equation of the cylindrical eccentric vibration system:

[0030]

[0031] In the above scheme, the fourth-order Runge-Kutta method discretizes the differential dynamic equations of the cylindrical eccentric vibration system as follows:

[0032]

[0033]

[0034] Where: K1, K2, K3, K4, L1, L2, L3, L4 are represented as:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Among them, t n and tn+1 These represent the nth and (n+1)th time steps, respectively, where Δt is the computation time step size. and These are the system's natural circular frequency and structural damping ratio, respectively; F(t) n ) for t n The force exerted at any given moment.

[0044] In the above scheme, step S7 uses a spring smoothing model and a mesh reconstruction model for the dynamic mesh.

[0045] The beneficial effects of this invention are as follows:

[0046] This invention, based on the commercial software Ansys / Fluent, takes the eccentric vibration of a marine drill string as its research background. It utilizes a self-compiled UDF program to further develop Fluent, numerically simulating the flow field under eccentric effects and the fluid-structure interaction between the rotating cylinder, and studying the vortex-induced vibration response of the cylinder. The flow field calculation employs the finite volume method to discretize the Reynolds-averaged incompressible Navier-Stokes equations. Structural analysis uses the fourth-order Runge-Kutta method to discretize and solve the differential dynamic equations of the eccentrically vibrating cylindrical system. These equations consider the dynamic equations under the coupling of eccentric force and fluid force. A mesh is constructed using a "rigid follower region + dynamic mesh region + static mesh region" approach, with the dynamic mesh employing a spring-smoothed model and a mesh reconstruction model. Fluid-structure interaction calculations are achieved through iterative interactive solutions between the fluid domain in Fluent and the solid domain in the UDF program. Compared with existing technologies, this invention provides a method for calculating the coupled vibration of a rotating cylinder's flow-induced vibration and inertial eddy currents, accurately reflecting the vortex-induced vibration response of an eccentrically rotating cylinder, and providing a foundation for the analysis of the vortex-induced vibration mechanism and response characteristics of marine drill strings. It also provides theoretical guidance for the development of vortex-induced vibration suppression technology for marine drill strings. Attached Figure Description

[0047] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0048] Figure 1 This is a schematic diagram of the principle of the method for calculating the coupled vibration of a rotating cylinder caused by flow and inertial eddy currents according to the present invention.

[0049] Figure 2 This is a flowchart of the method for calculating the coupled vibration of a rotating cylinder caused by flow and inertial eddy currents according to the present invention.

[0050] Figure 3 This is a schematic diagram of the numerical model and boundary conditions for the coupled vibration of a rotating cylinder caused by flow and inertial eddy currents in an embodiment of the present invention.

[0051] Figure 4 This is a diagram showing the coupled vibration region and mesh division of the rotating cylinder's flow-induced vibration and inertial eddy current vibration in an embodiment of the present invention.

[0052] Figure 5 This is a contour map of the vorticity of the flow field coupled with the inertial eddy current vibration of a rotating cylinder in an embodiment of the present invention; wherein, (ad) speed ratio (α) = 0; (eh) speed ratio (α) = 1, eccentricity ratio (e) = 0; (il) speed ratio (α) = 1, eccentricity ratio (e) = 0. . 1; (mp) speed ratio (α) = 1, eccentricity ratio (e) = 0.3;

[0053] Figure 6 This is a diagram showing the relationship between the transverse amplitude and reduced velocity of the coupled vibration of the rotating cylindrical flow-induced vibration and inertial eddy current in an embodiment of the present invention.

[0054] Figure 7 This is a graph showing the relationship between the downstream amplitude and reduced velocity of the coupled vibration of the rotating cylinder induced by flow and the inertial eddy current in an embodiment of the present invention.

[0055] Figure 8 This is a diagram showing the relationship between the wake eddy discharge mode of the coupled vibration of a rotating cylinder and inertial eddy current and the reduced velocity and eccentricity ratio in an embodiment of the present invention.

[0056] Figure 9 This is a diagram showing the relationship between the transverse amplitude, reduced velocity, and eccentricity ratio of the coupled vibration of the rotating cylindrical flow-induced vibration and inertial eddy current in an embodiment of the present invention. Detailed Implementation

[0057] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0058] This embodiment uses the coupled vibration of a low-mass-ratio rotating cylinder induced by flow and inertial eddy current in a laminar flow field as an example to illustrate the specific implementation method of the present invention, which includes the following steps:

[0059] S1. A two-dimensional numerical model of the coupled vibration of a rotating cylinder caused by flow and inertial eddy currents was established using ICEM CFD software, such as... Figure 3 As shown. The numerical model dimensions are 50D*70D (where D is the diameter of the cylinder), and the blocking rate is 2%.

[0060] S2. The numerical model was divided into regions and meshes using ICEM CFD software. The flow field from the cylindrical surface to the boundary consisted of a rigid region, a moving mesh region, and a static mesh region, as shown below. Figure 3 As shown; determine the mesh size and perform mesh generation. To realize the dynamic mesh model, the mesh type is triangular mesh; generate the boundary layer mesh on the cylindrical wall; generate the mesh file and import it into Fluent software.

[0061] S3. Compile a UDF secondary development program based on C language; the UDF program can set dynamic parameters such as the diameter, density, natural frequency, and damping coefficient of the structure; the UDF program can discretize and solve the differential dynamic equations of the cylindrical eccentric vibration system based on the fourth-order Runge-Kutta method; the UDF program is imported through the User Defined Functions window in Fluent software.

[0062] S4. In Fluent software, set the fluid parameters, boundary conditions, and solution parameters. The boundary conditions are set as follows: left boundary condition is velocity-inlet; right boundary condition is pressure-out; upper and lower boundary conditions are symmetry boundaries; and the cylindrical surface is a no-slip wall. Solution parameter settings include: turbulence model, solution algorithm, discretization scheme, solution accuracy, and time step.

[0063] To set up the dynamic mesh model, in the Fluent software's Dynamic Mesh window, select the Smoothing and Remeshing models; set the extraction lift coefficient (C). l ), drag coefficient (C) d ), transverse amplitude (A) y / D) and downstream amplitude (A) x Calculation data such as / D) are used to initialize the flow field model.

[0064] S5. Solve the flow field model using Fluent software. The flow field calculation is performed by discretizing the Reynolds-averaged incompressible Navier-Stokes equations using the finite volume method, thereby obtaining the flow field characteristics at time t0 and obtaining the load on the cylindrical surface.

[0065] S6. Based on the obtained cylindrical surface load, the force on the structure composed of the cylinder and the spring damping system is calculated by calling the macro Compute_Force_And_Moment through UDF. The result is then substituted into the differential dynamic equation (4) of the cylindrical eccentric vibration system. The equation (4) is then solved by calling the structural vibration response iteration program based on the fourth-order Runge-Kutta method through UDF, and the displacement, velocity and acceleration of the structure are obtained.

[0066] S7. The displacement, velocity, and acceleration of the structure are transmitted to the cylinder by calling the macro DEFINE_CG_MOTION through UDF, and the cylinder is given a rotational angular velocity by the macro DEFINE_CG_MOTION to realize the displacement and rotation of the cylinder boundary; the motion of the mesh boundary and the update of the mesh are realized through the dynamic mesh model.

[0067] S8 outputs the calculated data for lift coefficient, drag coefficient, cross-flow displacement, and downstream displacement at time t0.

[0068] S9. Determine if the termination condition has been met. If yes, end the calculation; otherwise, update the mesh and its boundaries, perform the flow field calculation at time t0+Δt, and repeat steps S5 to S9.

[0069] Finally, case and data files were exported using Fluent software; vorticity and velocity contour plots were analyzed and plotted using post-processing software such as Tecplot; and amplitude and hydrodynamic coefficient trend plots were analyzed and plotted using post-processing software such as Origin. In the given figures, Figure 5 The vorticity contour plot shows that as the eccentricity ratio e increases, especially when e = 0.3, the vorticity of the rotating cylinder decreases only at V. r =2 exhibits periodicity, in V r It loses its periodicity when the intervals are 6, 8, or 12. Figure 6 and Figure 7 The graphs show the relationship between transverse and longitudinal amplitudes and reduced velocity, respectively. For an eccentric cylinder, the transverse amplitude gradually increases as the eccentricity ratio e increases. Figure 8 The graph shows the relationship between the wake vortex shedding mode and the reduced velocity and eccentricity ratio. Figure 9 The graph shows the relationship between transverse amplitude, reduced velocity, and eccentricity ratio. Figure 8 and Figure 9 It was found that the 2S wake mode is mainly concentrated in the low amplitude region, while the mixed vortex shedding mode corresponds to the high amplitude region, and the vortex shedding in this region is not periodic.

[0070] In the numerical simulation process of this invention, if turbulence calculation is required, the k-ω model is selected; turbulent intensity and turbulent viscosity ratio are used to describe turbulence. For example, for a turbulent flow field with Re = 10000, the turbulent intensity is set to 5% and the turbulent viscosity ratio is set to 23.7.

[0071] In this invention, the flow field calculation is performed by discretizing the Reynolds-averaged incompressible Navier-Stokes equations using the finite volume method, and the structural dynamics equations are solved by discretizing the fourth-order Runge-Kutta method. The mesh is established using the approach of "rigid follower region + dynamic mesh region + static mesh region", and the dynamic mesh adopts the spring smoothing model and the mesh reconstruction model. Fluid-structure interaction calculation is achieved through iterative solving between the fluid domain in Fluent and the solid domain in the UDF program.

[0072] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0073] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for calculating the coupled vibration of a rotating cylinder caused by flow and inertial eddy currents, characterized in that, Includes the following steps: S1. Establish a two-dimensional numerical model of the coupled vibration of the rotating cylinder caused by flow and inertial eddy current. S2. Divide the numerical model into regions, with the flow field from the cylindrical surface to the boundary being a rigid region, a dynamic mesh region, and a static mesh region in sequence. Determine the mesh size and perform mesh generation; generate the mesh file and import it into Fluent software; S3. To realize the structural fluid-structure interaction calculation in Fluent software, compile a UDF secondary development program; set the cylinder dynamic parameters in the UDF secondary development program, and embed the UDF secondary development program into Fluent software; S4. Set the fluid parameters, boundary conditions, and solution parameters in Fluent software; S5. Solve the flow field model using Fluent software. The flow field calculation is performed by discretizing the Reynolds-averaged incompressible Navier-Stokes equations using the finite volume method, thereby obtaining the flow field characteristics in the model and acquiring the load on the cylindrical surface. S6. Based on the obtained cylindrical surface load, the forces on the structure composed of the cylinder and the spring damping system are calculated by UDF. The results are then substituted into the differential dynamic equation of the cylindrical eccentric vibration system. The structural vibration response program based on the fourth-order Runge-Kutta method is called to solve the differential dynamic equation of the cylindrical eccentric vibration system to obtain the displacement, velocity, and acceleration of the structure. The differential dynamic equation of the cylindrical eccentric vibration system is a differential dynamic equation that considers the coupling effect of eccentric force and fluid force, wherein: The governing equations of the cylindrical eccentric vibration system are: The cylinder is supported by a spring damping system, which includes a transverse linear elastic spring. And the flow direction linear elastic spring and cross-flow damping system and downstream damping system , Represents the elastic coefficient of the spring-damped system. The damping coefficient of the spring-damped system is represented by m, where m is the mass of the cylinder and t represents time. , , Let represent the dimensionless displacement, velocity, and acceleration of the cylinder in the transverse direction, respectively. , , Let represent the dimensionless displacement, velocity, and acceleration of the cylinder in the downstream direction, respectively. and These are the eccentric forces in the cross-flow direction and the downstream direction, respectively, and their magnitudes are related to the eccentricity E and the rotational speed. The direction is related to the cylinder's mass m and the rotation angle: The governing equation for the flow-induced vibration of a cylinder is: in, Represents the mass ratio of the cylinder. Represents the damping ratio. This represents the flow force coefficient on the cylindrical surface. ; This represents the crossflow force coefficient on the cylindrical surface. , , These represent the fluid forces experienced by the cylinder in the downstream and transverse directions, respectively. This represents the density of a cylinder. Indicates the diameter of the cylinder. Indicates the velocity of the fluid flowing downstream; The reduction rate is defined as follows: , The natural frequency of the cylinder; Adding equations (1) and (3) together yields the differential dynamic equation of the cylindrical eccentric vibration system: The fourth-order Runge-Kutta method discretizes the differential dynamic equations of the cylindrical eccentric vibration system as follows: in: Represented as: in, and These represent the nth and (n+1)th time steps, respectively. To calculate the time step, and These are the system's natural circular frequency and structural damping ratio, respectively. for The force applied at any given moment; S7. The displacement, velocity, and acceleration of the structure are transmitted to the cylinder through UDF to realize the displacement of the cylinder; the rotational angular velocity of the cylinder is defined through UDF to realize the rotation of the cylinder; the movement of the mesh boundary and the updating of the mesh are realized through the dynamic mesh model. S8. Output the calculation results of the cylinder, including transverse displacement, downstream displacement, lift and drag, through UDF and Fluent. S9. Determine whether the current cylindrical vibration is stable based on the output results. If it is, end the calculation; otherwise, solve the flow field for the next time step and repeat steps S5 to S9.

2. The method for calculating the coupled vibration of a rotating cylinder induced by flow and inertial eddy currents according to claim 1, characterized in that, In steps S1 and S2, ICEM CFD software is used for model building and mesh generation; a triangular mesh is used globally, and a boundary layer mesh is set on the cylindrical wall; the rigid region is the cylindrical wall and part of the boundary layer region, the dynamic mesh region is the region near the cylinder, and the other regions of the flow field are static mesh regions.

3. The method for calculating the coupled vibration of a rotating cylinder induced by flow and inertial eddy currents according to claim 1, characterized in that, In step S3, the set dynamic parameters of the cylinder include diameter, density, natural frequency, and damping coefficient.

4. The method for calculating the coupled vibration of a rotating cylinder caused by flow and inertial eddy currents according to claim 1, characterized in that, In step S4, the boundary conditions are as follows: the left boundary condition is the velocity inlet; the right boundary condition is the pressure outlet; the upper and lower boundary conditions are symmetrical boundaries; and the cylindrical surface is a non-slip wall.

5. The method for calculating the coupled vibration of a rotating cylinder caused by flow and inertial eddy currents according to claim 1, characterized in that, In step S4, the setting of the solution parameters includes: turbulence model, solution algorithm, discretization scheme, solution accuracy, and time step.

6. The method for calculating the coupled vibration of a rotating cylinder induced by flow and inertial eddy currents according to claim 1, characterized in that, In step S7, the dynamic mesh models used are the spring smoothing model and the mesh reconstruction model.

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