Flow-induced vibration prediction method for nonlinear cylinder system

Abstract

The invention discloses a nonlinear cylinder system flow-induced vibration prediction method, and belongs to the field of computational fluid mechanics numerical simulation. The method comprises the following steps: simplifying a rigidly connected double-cylinder system into a two-dimensional plane geometric model, and simplifying a vibration model into a nonlinear spring-damping-mass block model; establishing a two-dimensional drainage basin model surrounding the double-cylinder system; dividing a flow field domain grid and a structural domain grid by adopting a nested grid technology; establishing a flow-induced vibration model of the rigid connection double-cylinder system under the support of a nonlinear spring; updating a flow field grid based on nested grid dynamic interpolation, and performing fluid-structure interaction numerical calculation; and calculating to obtain the flow-induced vibration characteristics of the rigid connection double-cylinder system under the support of the nonlinear spring. According to the method, the problem that a linear model cannot reflect actual dynamic response is solved, and the prediction precision and the energy collection efficiency are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the field of numerical simulation of computational fluid dynamics, and particularly relates to a method for predicting the flow-induced vibration of a nonlinear cylinder system. Background Art

[0002] When a fluid flows past a nonlinear structure, periodic vortex shedding phenomena will alternately occur in the wakes on both sides of the structure, thereby generating periodically varying hydrodynamic forces on the transverse direction of the structure, and the elastic structure will also generate transverse vibrations due to this. This phenomenon is called vortex-induced vibration (VIV). When the vortex shedding frequency of the structure approaches the natural frequency of the structure, the "frequency lock-in" phenomenon will occur. When the "frequency lock-in" occurs, large-amplitude vibrations will be generated in the transverse direction of the structure, causing damage to the structure. Vortex-induced vibration widely exists in columnar structures such as the wind turbine tower barrels, bridge structures, high-rise buildings in wind engineering and the marine risers, platform columns in ocean engineering. If the structure is in the frequency lock-in state for a long time, the fatigue life of the structure will be greatly reduced.

[0003] When the structure vibrates under the action of the wake, it is called wake-induced vibration. Different from the typical vortex-induced vibration of a single cylinder, the vibration mechanism of the cylinder flow-induced vibration caused by the wake is more complex. The maximum amplitude of the cylinder structure caused by wake-induced vibration usually exceeds the maximum amplitude that can be caused by typical vortex-induced vibration, which poses a greater threat to the safety of the cylinder structure. The vortex-induced vibration of a circular cylinder is a combination of forced vibration and self-excited vibration, with self-limiting characteristics; but under the action of the wake, the circular cylinder will generate galloping. Galloping has the characteristics of large amplitude, and the vibration amplitude during galloping increases continuously with the increase of the reduced velocity. At the same time, the flow-induced vibration under the action of the wake is subjected to periodic fatigue stress, and the large-amplitude transverse vibration generated will cause fatigue damage, and even structural failure problems may occur at high wind speeds.

[0004] In ocean engineering, ocean structures often appear in the form of multi-cylinder coupling. For example, in structures such as submarine oil pipelines and underwater suspension tunnels, the pipelines form a double-cylinder system through rigid connections, and they vibrate synchronously with the same displacement. At the same time, due to the mutual influence between adjacent pipe bodies, the vortex-induced vibration characteristics of the rigidly connected double-cylinder system are complex. The traditional vortex-induced vibration model is a linear spring-supported cylinder system, and using a nonlinear spring to replace the linear spring will affect the vortex-induced vibration characteristics of the cylinder system, enabling it to maintain a higher amplitude level in a wider velocity range and improving the energy harvesting efficiency. Summary of the Invention

[0005] Technical Problems to be Solved

[0006] To avoid the deficiencies of the prior art, the present invention provides a method for predicting the flow-induced vibration of a nonlinear cylinder system. A double-cylinder system rigidly connected with a cubic nonlinear spring support is used to establish a two-degree-of-freedom dynamic model, and the vibrations in the cross-flow direction and the in-line direction are considered simultaneously. The prediction of the flow-induced vibration of the rigidly connected double-cylinder system solves the problem that the linear model cannot reflect the actual dynamic response, and significantly improves the prediction accuracy and energy harvesting efficiency.

[0007] The technical solution of the present invention is as follows: A method for predicting the flow-induced vibration of a nonlinear cylinder system, and the specific steps are as follows:

[0008] Simplify the rigidly connected double-cylinder system into a two-dimensional plane geometric model, and simplify the vibration model into a nonlinear spring-damper-mass model, where the restoring force of the nonlinear spring satisfies the cubic nonlinear relationship;

[0009] Establish a two-dimensional flow domain model surrounding the double-cylinder system, and the two-dimensional flow domain is a rectangle surrounding the cylinder system;

[0010] Adopt the nested grid technology to divide the flow field domain and the structure domain grids. The component grid wrapping the double cylinders is a circular area, and the center of the circular area is the midpoint of the connection line of the double-cylinder system. The background grid is encrypted near the cylinder area and sparse away from the area;

[0011] Establish a flow-induced vibration model of the rigidly connected double-cylinder system supported by a nonlinear spring, including the flow field control equation and the two-degree-of-freedom dynamic equation of the structure field. The expression of the two-degree-of-freedom dynamic equation of the structure field is as follows:

[0012]

[0013] Among them, m is the mass of the cylinder, c is the structural damping coefficient, k1 is the linear spring stiffness, k2 is the nonlinear spring stiffness, respectively represent the accelerations of the cylinder in the in-line direction and the cross-flow direction, respectively represent the velocities of the cylinder in the in-line direction and the cross-flow direction, x and y respectively represent the displacements of the cylinder in the in-line direction and the cross-flow direction, F D is the drag force on the cylinder, F L is the lift force on the cylinder;

[0014] Based on the nested grid dynamic interpolation to update the flow field grid, and use the Runge-Kutta method to solve the two-degree-of-freedom dynamic equation of the structure field to realize the fluid-structure coupling numerical calculation of the double-cylinder system supported by the nonlinear spring;

[0015] Post-process the data obtained from the fluid-structure coupling numerical calculation, extract the displacement, velocity response and flow field structure information of the double-cylinder system, and obtain the flow-induced vibration characteristics of the rigidly connected double-cylinder system supported by the nonlinear spring.

[0016] A further technical solution of the present invention is that the restoring force of the non-linear spring satisfies the relational expression: F = k2y 3 .

[0017] A further technical solution of the present invention is that the stiffness ratio of the non-linear spring to the cylinder is:

[0018]

[0019] where D represents the diameter of the cylinder in the double-cylinder system.

[0020] A further technical solution of the present invention is that in the nested grid technology, the diameter of the circular area of the component grid is 8D, where D represents the diameter of the cylinder in the double-cylinder system; the background grid divides the boundary layer grid (Y + <1) near the cylinder.

[0021] A further technical solution of the present invention is that the center distance between the two cylinders of the double-cylinder system is 5D, the synchronous displacement occurs during vibration, and the coupling effect of vibration in the flow direction and the cross-flow direction is transmitted through the cubic non-linear spring.

[0022] A further technical solution of the present invention is that the inlet boundary of the two-dimensional flow domain is 10D away from the front cylinder, the outlet boundary is 19D away from the rear cylinder, and the upper and lower boundaries are both 10D away from the cylinder.

[0023] A further technical solution of the present invention is that the expression of the flow field control equation is as follows:

[0024]

[0025] where, ρ f is the density of the incompressible fluid; x i and x j respectively represent the i-direction and the j-direction in the Cartesian coordinate. u i and u j respectively represent the instantaneous velocity components in the i-direction and the j-direction, u i ′ and u′ j are the velocity pulsations in the i-direction and the j-direction, and are the time averages of the velocities in the i-direction and the j-direction; t, p, μ respectively represent time, pressure, kinematic viscosity, is the Laplace operator; μ t is the turbulent viscosity, and the subscript "t" represents turbulence; k t is the turbulent kinetic energy; δ ij is the "Kronecker delta" symbol, that is, when i = j, δij = 1, and when i ≠ j, δ ij = 0.

[0026] A further technical solution of the present invention is that the inlet of the flow field adopts a velocity inlet, and the given fluid incoming velocity is a uniform velocity; the outlet is selected as a pressure outlet, and the average static pressure is the standard atmospheric pressure; the surface of the cylinder is a non-slip and smooth wall boundary condition; the boundary of the flow field region adopts a symmetric boundary.

[0027] A further technical solution of the present invention is that the method for dynamically interpolating and updating the flow field grid by nested grids is to feedback the cylinder displacement to the flow field grid, and map the variable information of the background grid to the component grid boundary through an interpolation algorithm.

[0028] A prediction model for flow-induced vibration of a nonlinear cylinder system includes the following functional units:

[0029] Geometric modeling unit: used to simplify the rigidly connected double-cylinder system into a two-dimensional plane geometric model, and establish a two-dimensional watershed model surrounding the double-cylinder. The inlet boundary of the watershed is 10D away from the front cylinder, the outlet boundary is 19D away from the rear cylinder, and the upper and lower boundaries are both 10D away from the cylinder.

[0030] Grid division unit: adopts nested grid technology to divide the grid of the watershed, including a circular component grid with the midpoint of the double-cylinder connection line as the center and an outer background grid. The background grid in the area close to the cylinder is encrypted, and the grid size gradually increases away from the area.

[0031] Fluid-structure interaction calculation unit: establishes a flow-induced vibration model of a rigidly connected double-cylinder system under nonlinear spring support, including a flow field control equation and a two-degree-of-freedom dynamics equation of the structure field; updates the cylinder displacement in real time based on the Runge-Kutta method, and dynamically adjusts the flow field grid through nested grid interpolation technology.

[0032] Post-processing unit: used to extract the displacement and velocity response curves of the double-cylinder system and the vorticity and pressure distribution data of the flow field, and output the amplitude prediction results and energy harvesting efficiency evaluation reports within a wide flow velocity range.

[0033] Beneficial effects

[0034] The beneficial effects of the present invention are as follows:

[0035] (1) By introducing nonlinear spring support, the present invention solves the problem that the existing linear spring model cannot accurately simulate the dynamic response of the cylinder, thereby improving the prediction accuracy of vortex-induced vibration (as Figure 1 shown). At the same time, the nonlinear spring enables the cylinder system to maintain a higher amplitude within a wider flow velocity range, thereby improving the energy harvesting efficiency of the cylinder system and meeting the requirements of practical applications. The stiffness of the nonlinear spring changes adaptively with the amplitude, enabling the double-cylinder system to maintain stable vibration characteristics within a wide flow velocity range.

[0036] (2) The present invention realizes the prediction of the flow-induced vibration of a rigidly connected double-cylinder system supported by a non-linear spring by establishing a structural dynamics model of the flow-induced vibration of the system, thereby improving the energy harvesting efficiency compared with the linear spring support system (as shown in Figure 7 ), and is applicable to scenarios such as self-powered ocean monitoring equipment. By accurately considering the interaction between the fluid and the cylinder system based on fluid-structure interaction, the accuracy of the prediction of vortex-induced vibration is improved. It can not only obtain the structural deformation and transient flow field information, but also greatly reduce the number of experiments and save the experimental cost.

[0037] (3) The present invention adopts the nested grid technology and a refined flow field modeling method to solve problems such as the grid distortion caused by the large amplitude of the cylinder and the failure of the solution due to the negative grid problem, thereby improving the calculation efficiency. A high-fidelity simulation model of the flow-induced vibration of a rigidly connected double-cylinder system supported by a non-linear spring is established, and the numerical prediction results have a certain degree of accuracy.

[0038] (4) The present invention, through a two-degree-of-freedom dynamics model (the coupled equations in the cross-flow direction and the in-line direction), simultaneously considers the synchronous vibration of the double-cylinder and the non-linear fluid force, capturing more details of the vibration energy transfer than the single-degree-of-freedom model (as shown in Figure 6 ), providing high-fidelity data support for the structural optimization under complex flow fields.

[0039] (5) The present invention replaces physical experiments with fluid-structure interaction numerical simulations, reducing the number of experiments and shortening the R & D cycle while ensuring the prediction accuracy, especially applicable to the vibration safety assessment of large-scale ocean structures (such as the pile foundation of cross-sea bridges and deep-sea risers). Description of the Drawings

[0040] Figure 1 is a comparison of the amplitude prediction data and experimental amplitude data of a single-cylinder system supported by a linear spring and a non-linear spring at different reduced velocities.

[0041] Figure 2 is a schematic flow chart of a fluid-structure interaction prediction method for the flow-induced vibration of a non-linear cylinder system in an embodiment of the present invention.

[0042] Figure 3 is a simplified schematic diagram of the flow-induced vibration model of a rigidly connected double-cylinder system in an embodiment of the present invention.

[0043] Figure 4 is a schematic diagram of the grid division of the flow field domain of a rigidly connected double-cylinder structure in an embodiment of the present invention.

[0044] Figure 5 is the amplitude distribution of a rigidly connected double-cylinder system supported by a linear spring or a non-linear spring at different reduced velocities.

[0045] Figure 6 It is the vorticity contour of a rigidly connected double-cylinder system supported by a nonlinear spring at different reduced velocities.

[0046] Figure 7 It is the energy harvesting efficiency contour of a rigidly connected double-cylinder system supported by a nonlinear spring at different damping ratios and Reynolds numbers.

[0047] Explanation of reference numerals: 1. Damping, 2. Rigidly connected double-cylinder, 3. Nonlinear spring. Detailed implementation manners

[0048] The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present invention and should not be construed as a limitation to the present invention.

[0049] Traditional technologies usually use a linear spring model to describe the elastic behavior of a cylinder system. The stiffness of a linear spring is constant at different vibration amplitudes and cannot reflect the existing nonlinear elastic characteristics in reality. While the present method uses a nonlinear spring to replace the linear spring. The stiffness of the nonlinear spring varies with the amplitude and can more realistically reflect the dynamic response of the cylinder at different vibration amplitudes. This improvement enables the cylinder system to maintain a higher amplitude within a wider flow velocity range, thereby improving the energy harvesting efficiency. At the same time, by introducing nested grid technology, fine grid division, and fluid-structure interaction calculation methods, the calculation efficiency has been significantly improved, especially in the case of large-amplitude vibration, and high accuracy and stability can be maintained. Since the present invention is a cylinder system supported by a nonlinear spring, a fluid-structure interaction prediction method for the flow-induced vibration of a rigidly connected double-cylinder system supported by a nonlinear spring is proposed.

[0050] For example, for the vibration analysis of a single cylinder or a double cylinder under the action of a fluid, the prior art uses a linear spring model and adopts weak coupling or strong coupling methods for fluid-structure interaction calculation. Its focus is on dealing with wake-induced vibration, using ANSYS Fluent for simulation, grid division, and dynamic grid technology, but does not mention a nonlinear spring.

[0051] For example, the prior art reduces vibration by introducing a nonlinear energy well of a cubic nonlinear spring. Although it involves a nonlinear element, the purpose is to suppress vibration rather than predict vibration characteristics, and the structure is a tandem double-cylinder. For a tandem double-cylinder (non-rigidly connected), the upstream and downstream cylinders move independently, and there is wake interference. Therefore, the vibration analysis of a rigidly connected double-cylinder cannot be obtained.

[0052] Based on the problems existing in the above prior art, the present invention proposes a method for predicting the flow-induced vibration of a nonlinear cylinder system, and the specific steps are as follows:

[0053] Step 1: Simplify the rigidly connected double-cylinder system into a two-dimensional planar geometric model, and simplify the vibration model into a nonlinear spring-damper-mass model, where the restoring force of the nonlinear spring satisfies the cubic nonlinear relationship;

[0054] Step 2: Establish a two-dimensional flow domain model surrounding the double-cylinder system. The two-dimensional flow domain is a rectangle surrounding the cylinder system;

[0055] Step 3: Use the nested grid technology to divide the grids of the flow field domain and the structure domain. The component grid wrapping the double-cylinder is a circular area, and the center of the circular area is the midpoint of the connection line of the double-cylinder system. The background grid is encrypted near the cylinder area and sparse far away from the area;

[0056] Step 4: Establish a fluid-induced vibration model of the rigidly connected double-cylinder system supported by a nonlinear spring, including the flow field control equation and the two-degree-of-freedom dynamic equation of the structure field. The expression of the two-degree-of-freedom dynamic equation of the structure field is as follows:

[0057]

[0058] where m is the mass of the cylinder, c is the structural damping coefficient, k1 is the linear spring stiffness, k2 is the nonlinear spring stiffness, respectively represent the accelerations of the cylinder in the downstream and cross-stream directions, respectively represent the velocities of the cylinder in the downstream and cross-stream directions, x and y respectively represent the displacements of the cylinder in the downstream and cross-stream directions, and F D is the drag force on the cylinder, and F L is the lift force on the cylinder;

[0059] Step 5: Update the flow field grid based on the nested grid dynamic interpolation, and use the Runge-Kutta method to solve the two-degree-of-freedom dynamic equation of the structure field to realize the fluid-structure coupling numerical calculation of the double-cylinder system supported by a nonlinear spring;

[0060] Step 6: Post-process the data obtained from the fluid-structure coupling numerical calculation, extract the displacement, velocity response and flow field structure information of the double-cylinder system, and obtain the fluid-induced vibration characteristics of the rigidly connected double-cylinder system supported by a nonlinear spring.

[0061] Through the coupled modeling of the nonlinear spring and the rigidly connected double-cylinder, the present invention avoids the failure of the traditional linear model in predicting a wide flow velocity range. Through the component grid 8D diameter and the dynamic interpolation technology, the grid distortion caused by vibration is overcome to ensure the calculation convergence. Through the collaborative innovation of the nonlinear spring, the nested grid and the two-degree-of-freedom model, comprehensive breakthroughs are achieved in prediction accuracy, calculation efficiency, energy harvesting and engineering applicability, and the core bottleneck problems of the traditional linear model and the vibration suppression technology are solved.

[0062] The above technical solution will be further described below in conjunction with the accompanying drawings:

[0063] In one embodiment, the parameter Figure 2 As shown, a fluid-structure interaction prediction method for the flow-induced vibration of a non-linear cylinder system in this embodiment includes the following steps:

[0064] Step 1: Refer to Figure 3 As shown, ignoring the deformation in the axial direction of the structure, the three-dimensional structure is simplified into a geometric model on a two-dimensional plane, and the vibration model is simplified into a spring-damper-mass model to complete the geometric modeling of the rigidly connected double-cylinder system; then, according to the position of the cylinder system, a two-dimensional flow domain model is established; the two-dimensional flow domain is a rectangle surrounding the cylinder system;

[0065] Step 2: Refer to Figure 4 As shown, finite element mesh division is performed on the structural domain and the flow field domain respectively; first, component meshes are divided for the part wrapping the cylinder, the center of the component mesh is the midpoint of the center connection line of the cylinder system, and the boundary is a circular area surrounding the cylinder system; background meshes are divided for the external flow field, the meshes are dense in the area close to the cylinder and sparse in the area far from the cylinder; the structural domain mesh and the flow field domain mesh are interpolated to form a flow field calculation mesh;

[0066] Step 3: Establish a flow-induced vibration model for the rigidly connected double-cylinder system supported by non-linear springs;

[0067] Step 4: Fluid-structure interaction calculation;

[0068] First, determine the initial conditions and boundary conditions. The velocity inlet is used at the inlet of the flow field, and the given fluid incoming velocity is a uniform velocity; the pressure outlet is selected at the outlet, and the average static pressure is the standard atmospheric pressure; the surface of the cylinder is a no-slip and smooth wall boundary condition; the symmetric boundary is used for the boundary of the flow field region; then, in the CFD solver, solve the fluid control equation to obtain the velocity of the flow field and the force acting on the cylinder, substitute the force generated by the fluid acting on the cylinder into the flow-induced vibration model of the double-cylinder system, and use the Runge-Kutta method to solve the displacement and velocity at the next moment; then, based on the nested grid technology, update the flow field mesh with the motion velocity and displacement of the double-cylinder system to obtain a new flow field calculation mesh for the flow field numerical calculation at the next time step, and realize the fluid-structure interaction numerical calculation of the double-cylinder system;

[0069] Step 5: When the simulation time is reached, post-process the calculated data, extract the displacement and velocity response curves of the double-cylinder system and the flow field structure information of the flow field domain, and obtain the flow-induced vibration characteristics of the rigidly connected double-cylinder system supported by non-linear springs.

[0070] Specifically, in step one, the inlet boundary of the rectangle is 10D away from the previous cylinder, the outlet boundary is 19D away from the next cylinder, the upper and lower boundaries of the cylinder are both 10D, and the outer boundary diameter of the component grid surrounding the cylinder is 8D.

[0071] Specifically, in step two, all the finite element meshes used are structured meshes, and the part close to the cylinder surface is the boundary layer mesh (Y + <1).

[0072] Specifically, the specific establishment method of the calculation model in step three is as follows:

[0073] The fluid-induced vibration model of the rigidly connected double-cylinder system under the nonlinear spring support includes the flow field control equation and the structural field cylinder system model control equation;

[0074] In the flow field, based on the CFD method, the flow field domain is solved, and the unsteady incompressible fluid RANS equation is:

[0075]

[0076]

[0077] In Equation (2),

[0078]

[0079] In the formula, ρ f is the density of the incompressible fluid; x i and x j respectively represent the i-direction and j-direction in the Cartesian coordinate. u i and u j respectively represent the instantaneous velocity components in the i-direction and j-direction, u i ′ and u′ j are the velocity pulsations in the i-direction and j-direction, and are the time averages of the velocities in the i-direction and j-direction; t, p, μ respectively represent time, pressure, and kinematic viscosity, is the Laplace operator; μ t is the turbulent viscosity, and the subscript "t" represents turbulence; k t is the turbulent kinetic energy; δ ij is the "Kronecker delta" symbol, that is, when i = j, δij = 1, and when i ≠ j, δ ij = 0; the SST k–ω turbulence model is selected for the turbulence model; by calculating the flow field, the pressure distribution on the two-dimensional cylinder surface can be obtained, and further the lift and drag coefficients acting on the two-dimensional cylinder can be obtained;

[0080] For a cubic nonlinear spring, the nonlinear restoring force satisfies the relation: F = k2y 3 , where k2 is the stiffness of the cubic nonlinear spring. Then, the structural dynamic equations in the downstream and cross-stream directions for a structure with cubic nonlinear springs are:

[0081]

[0082]

[0083] In the equations, m is the mass of the cylinder, c is the structural damping coefficient, k1 is the linear spring stiffness, k2 is the nonlinear spring stiffness, is the acceleration of the cylinder, is the velocity of the cylinder, x and y are the displacements of the cylinder, F D is the drag force on the cylinder, F L is the lift force on the cylinder.

[0084] After nondimensionalization, the corresponding structural dynamic equations are:

[0085]

[0086]

[0087] In the equations, the natural frequency of the cylinder The damping ratio where D is the diameter of the cylinder.

[0088] Specifically, in step two, the nested grid technique is used to perform structured grid division on the boundary of the cylinder system and the flow field respectively, and then the overlapping part of the two sets of grids is interpolated, and the boundary element variable information in the background region is interpolated to the boundary elements in the nested region to complete the flow field calculation grid; in step four, the nested grid technique is used to update the flow field grid, and the moved component grids are re-interpolated with the flow field domain grid to form a new flow field calculation grid, and the nested grid technique is used to establish a fluid-induced vibration simulation model for the double-cylinder system.

[0089] Specifically, in the double-cylinder system, the support spring type is a nonlinear spring, the influence of the nonlinear spring on the vibration of the double-cylinder system is considered, the structural dynamic equations of the rigidly connected double-cylinder system supported by the nonlinear spring are completed, and a fluid-induced vibration numerical simulation model of the rigidly connected double-cylinder system supported by the nonlinear spring is established.

[0090] In one embodiment, a simulation model is established for the single-cylinder system: the mass of the single-cylinder system m = 2.7325 kg, the linear stiffness k = 17.26 N / m, the nonlinear stiffness k2 = 655.88 N / m, the damping ratio ζ = 0.00542, the diameter D = 0.02 m, and the natural frequency f n= 0.4 Hz, the amplitude distributions of the single-cylinder system supported by linear springs or nonlinear springs are calculated at various reduced velocities and compared with the experimental data. It can be found through comparison that, compared with linear springs, nonlinear springs can better reflect the characteristics of the vortex-induced vibration of the cylinder system and improve the prediction accuracy of vortex-induced vibration (as Figure 1 shown).

[0091] In one embodiment, a simulation model of a rigidly connected double-cylinder system is established: the mass m of the rigidly connected double-cylinder system is 2.7325 kg, the linear stiffness k1 is 17.26 N / m, the nonlinear stiffness is k2 = 655.88 N / m, the damping ratio ζ is 0.00542, the diameter D is 0.02 m, and the natural frequency f n = 0.4 Hz, and the fluid-induced vibration characteristics of the cylinder system supported by linear springs or nonlinear springs are calculated at various reduced velocities (as Figure 5 , Figure 6 and Figure 7 shown).

[0092] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and purposes of the present invention.

Claims

1. A prediction method for flow-induced vibration of a non-linear cylinder system, characterized in that The specific steps are as follows: Simplify the rigidly connected double-cylinder system into a two-dimensional plane geometric model, and simplify the vibration model into a nonlinear spring-damper-mass model, where the restoring force of the nonlinear spring satisfies the cubic nonlinear relationship; Establish a two-dimensional flow domain model surrounding the double-cylinder system. The two-dimensional flow domain is a rectangle surrounding the cylinder system; Use the nested grid technology to divide the grids of the flow field domain and the structure domain. The component grid wrapping the double cylinders is a circular area, and the center of the circular area is the midpoint of the connection line of the double-cylinder system. The background grid is encrypted near the cylinder area and sparse away from the area; Establish a fluid-induced vibration model of the rigidly connected double-cylinder system supported by nonlinear springs, including the flow field control equation and the two-degree-of-freedom dynamics equation of the structure field. The expression of the two-degree-of-freedom dynamics equation of the structure field is as follows: where m is the mass of the cylinder, c is the structural damping coefficient, k1 is the linear spring stiffness, and k2 is the nonlinear spring stiffness, represent the accelerations of the cylinder in the along - flow direction and the cross - flow direction respectively, represent the velocities of the cylinder in the along - flow direction and the cross - flow direction respectively, x and y represent the displacements of the cylinder in the along - flow direction and the cross - flow direction respectively, and F D is the drag force acting on the cylinder, and F L is the lift force acting on the cylinder; Based on the nested grid dynamic interpolation to update the flow field grid, and use the Runge-Kutta method to solve the two-degree-of-freedom dynamics equation of the structure field to realize the fluid-structure coupling numerical calculation of the double-cylinder system supported by nonlinear springs; Post-process the data obtained from the fluid-structure coupling numerical calculation, extract the displacement, velocity response of the double-cylinder system and the flow field structure information, and obtain the fluid-induced vibration characteristics of the rigidly connected double-cylinder system supported by nonlinear springs.

2. The flow-induced vibration prediction method for a non-linear cylinder system according to claim 1, wherein: The restoring force of the non-linear spring satisfies the relation: F = k2y 3 .

3. The flow-induced vibration prediction method for a non-linear cylinder system according to claim 1, characterized in that: The stiffness ratio of the nonlinear spring to the cylinder is: where D represents the diameter of the cylinder in the double-cylinder system.

4. The flow-induced vibration prediction method for a non-linear cylinder system according to claim 1, wherein: In the nested grid technique, the diameter of the circular region of the component grid is 8D, where D represents the diameter of the column in the double-column system; the background grid divides the boundary layer grid Y near the column + <1.

5. The prediction method of fluid-induced vibration of a non-linear cylinder system according to claim 4, wherein: The center distance between the two cylinders of the double-cylinder system is 5D, and the synchronous displacement occurs during vibration. The coupling effect of the vibration in the flow direction and the cross-flow direction is transmitted through the cubic nonlinear spring.

6. The method for predicting the flow-induced vibration of a non-linear cylinder system according to claim 5, characterized in that: The inlet boundary of the two-dimensional flow domain is 10D away from the front cylinder, the outlet boundary is 19D away from the rear cylinder, and the upper and lower boundaries are both 10D away from the cylinder.

7. The flow-induced vibration prediction method for a non-linear cylinder system according to claim 1, characterized in that: The expression of the flow field control equation is as follows: Among them, ρ f is the density of the incompressible fluid; x i and x j respectively represent the i-direction and the j-direction in the Cartesian coordinates. u i and u j respectively represent the instantaneous velocity components in the i-direction and the j-direction, u i ′ and u′ j are the velocity pulsations in the i-direction and the j-direction, and are the time-averaged values of the velocities in the i-direction and the j-direction; t, p, μ respectively represent time, pressure, and kinematic viscosity, is the Laplace operator; μ t is the turbulent viscosity, and the subscript "t" represents turbulence; k t is the turbulent kinetic energy; δ ij is the "Kronecker delta" symbol, that is, when i = j, δij = 1, and when i ≠ j, δ ij = 0.

8. The flow-induced vibration prediction method for a non-linear cylinder system according to claim 1, characterized in that: The inlet of the flow field adopts a velocity inlet, and the given fluid incoming velocity is a uniform velocity; the outlet selects a pressure outlet, and the average static pressure is the standard atmospheric pressure; the surface of the cylinder is a no-slip and smooth wall boundary condition; the boundary of the flow field area adopts a symmetric boundary.

9. The method for predicting the flow-induced vibration of a non-linear cylinder system according to claim 1, characterized in that: The method for updating the flow field grid by nested grid dynamic interpolation is to feedback the cylinder displacement to the flow field grid, and map the variable information of the background grid to the component grid boundary through the interpolation algorithm.

10. A prediction model for flow-induced vibration of a non-linear cylinder system, which is used to implement the flow-induced vibration prediction method of a non-linear cylinder system according to any one of claims 1-9; characterized in that It includes the following functional units: Geometric modeling unit: used to simplify the rigidly connected double-cylinder system into a two-dimensional plane geometric model, and establish a two-dimensional flow domain model surrounding the double cylinders. The inlet boundary of the flow domain is 10D away from the front cylinder, the outlet boundary is 19D away from the rear cylinder, and the upper and lower boundaries are both 10D away from the cylinder; Grid division unit: use the nested grid technology to divide the grids of the flow domain, including a circular component grid with the midpoint of the connection line of the double cylinders as the center and the surrounding background grid. The background grid near the cylinder area is encrypted, and the grid size gradually increases away from the area; Fluid-structure coupling calculation unit: establish a fluid-induced vibration model of the rigidly connected double-cylinder system supported by nonlinear springs, including the flow field control equation and the two-degree-of-freedom dynamics equation of the structure field; Based on the Runge-Kutta method, the cylinder displacement is updated in real time, and the flow field grid is dynamically adjusted through the nested grid interpolation technology; Post-processing unit: used to extract the displacement and velocity response curves of the double-cylinder system, as well as the vorticity and pressure distribution data of the flow field, and output the amplitude prediction results within a wide flow velocity range and the energy harvesting efficiency evaluation report.

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