CN111177926B - Vortex-induced vibration forecasting method in pipe laying process - Google Patents
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Abstract
The embodiment of the invention discloses a method for forecasting vortex-induced vibration in a pipe laying process, which comprises the steps of modeling a flexible vertical pipe and solving the model; the modeling the flexible riser comprises: a1, obtaining a three-dimensional coupled structure motion equation and a wake vortex oscillator equation; a2, determining the boundary condition of the model; wherein the boundary conditions simulate dynamic behavior of the lowering riser; a3, determining the initial conditions of the model; the solving the model comprises: and numerically solving the structural motion equation and the wake vortex oscillator equation based on the boundary condition and the initial condition so as to forecast the vortex-induced vibration. The embodiment of the invention can be applied to the condition of lowering the stand pipe, can be widely applied to the industry and can provide reference for design and constructors.
Description
Technical Field
The invention relates to the technical field of vortex-induced vibration, in particular to a method for forecasting vortex-induced vibration in a pipe laying process.
Background
China always highly pays attention to ocean economic development, and south China always develops resources at strategic height. The south China sea has the most abundant offshore oil and gas resources, so the development of the oil and gas resources of the south China sea is valued by various relevant departments and various provinces and cities along the south China sea. The development of offshore oil and gas resources cannot be separated from risers with various types and functions. Risers play an important role in offshore oil and gas production as an important component for connecting offshore production platforms (as well as various types of floating production systems) to subsea production systems. Due to the superior performance and the more convenient construction method of the Steel Catenary (SCR) riser compared with the conventional riser, the SCR riser is widely applied to marine oil and gas development operation in China. However, the SCR riser is subject to the action of ocean currents during the lowering of the umbilical, and vortex-induced vibration occurs. The vortex-induced vibration is structural body vibration caused by wake vortexes periodically and alternately shedding generated by water flow flowing through the structural body, strength damage can be caused by overlarge vibration, fatigue damage can be generated even by vibration with small amplitude under the long-term action, and the safety of a riser and even the whole oil platform is threatened. Therefore, the method has important significance in forecasting the vortex-induced vibration generated in the process of lowering the SCR riser.
Numerical prediction of riser vortex-induced vibration at home and abroad generally comprises two methods, namely a Computational Fluid Dynamics (CFD) method and a semi-empirical model method. The CFD method can give all details of the flow field around the cylinder unambiguously, and reliably estimate the lift and drag experienced by the cylinder, but consumes significant computational resources to simulate the higher reynolds number case. The semi-empirical wake vortex vibrator model couples a structural motion equation and a vibrator equation for simulating vortex shedding, and the VIV is empirically predicted by using data measured in a vibration test, so that the calculation speed is high, and the understanding of the VIV physical mechanism is facilitated to be enhanced. The application of a wake vortex oscillator model to forecast the vortex-induced vibration of a riser is reported In a paper (Feng, Y.L., Li.S.W. & Chen, D.Y.. predictionfor combined In-Line and Cross-Flow VIV responses with a novel model for estimation of tension, 191 vol.1), and the method can approximately forecast the vibration of the riser during the service period, such as the forecast of the vibration amplitude, the vibration frequency and the vibration mode, by simplifying the boundary condition of the riser into a condition of two-end hinge joint, but cannot be applied to the vortex-induced vibration condition of the riser In the lowering process because the boundary condition of the two ends of the method is hinge joint.
The above background disclosure is only for the purpose of assisting understanding of the inventive concept and technical solutions of the present invention, and it is not necessarily prior art to the present invention, and should not be used for evaluating the novelty and inventive step of the present invention without explicit evidence to suggest that the above content has been disclosed at the filing date of the present invention.
Disclosure of Invention
The invention provides a vortex-induced vibration forecasting method in a pipe laying process, which can calculate vortex-induced vibration response in the pipe laying process of a flexible pipe cable.
In a first aspect, the present application provides a method for vortex-induced vibration forecasting during pipe laying, comprising modeling a flexible riser and solving the model; the modeling the flexible riser comprises: a1, obtaining a three-dimensional coupled structure motion equation and a wake vortex oscillator equation; a2, determining the boundary condition of the model; wherein the boundary conditions simulate dynamic behavior of the lowering riser; a3, determining the initial condition of the model; the solving the model comprises: and numerically solving the structural motion equation and the wake vortex oscillator equation based on the boundary condition and the initial condition so as to forecast the vortex-induced vibration.
In some preferred embodiments, the structural equation of motion is:
the mass M comprises a vertical pipe mass and an additional mass, R is the displacement of the vertical pipe, t is time, z is the height of the vertical pipe, R is damping, and EI is the rigidity of the vertical pipe; t is the tension of the stand pipe, and F is the exciting force;
the wake vortex oscillator equation is:
where p is the variable associated with wake vortex, q is the variable associated with wake vortex, Ax,Ay,εx,εyAs an empirical parameter, ΩfFor vortex shedding frequency, D is the diameter of the riser, x is the displacement of the riser in the forward direction, and y is the displacement of the riser in the cross-flow direction.
In some of the preferred embodiments of the present invention,
r=x+iy (2)
F=Fx+iFy (3)
Fx=fD+f′D (4)
R=Rs+Rf=2ξdMΩs+γρD2Ωf (6)
the displacement r and the exciting force F are expressed by complex numbers, i is an imaginary unit; the displacement r is decomposed into displacement in the forward flow direction x and the transverse flow direction y; the excitation force F is the fluid force exerted on the riser and can be decomposed into FxAnd Fy(ii) a External force F in x-directionxIs the average resistance fDAnd oscillation resistance fD' sum of; the mass M comprises a structural mass MsAnd an additional mass; ca is an additional mass coefficient, considered as a constant, the variation of which is ignored; rho is the density of the seawater; d is the diameter of the stand pipe; the damping R is decomposed into structural damping RsAnd additional damping Rf(ii) a Gamma is a constant; xidIs a damping ratio; omegafFor vortex shedding frequency, ΩfIs calculated by the formulaWhere St is the Strouhal number, U is the flow rate, ΩnThe natural vibration circle frequency of the vertical pipe in the air; characteristic natural frequency omega of the risersAdopting natural frequency in water; the stiffness EI is assumed to be constant along the length of the riser cylinder; the tension T varies with arc length.
In some preferred embodiments, the drag coefficient of the fixed cylinder is calculated when the external force on the riser cylinder is calculatedIs calculated by the formula CD0(1+Kq2) (ii) a K is an amplification factor; cD0The average drag coefficient of the fixed cylinder; q is a variable related to wake vortexes and is related to the magnitude of lift force; acting on a circle of unit lengthResistance on the cylinder fDThe calculation formula of (2) is as follows:
resistance to oscillation fD' and lift force FyThe calculation formula of (c) is:
wherein, the oscillation resistance coefficient CDiAnd coefficient of lift CLThe calculation formula of (2) is as follows:
wherein, CDi0Amplitude of the oscillation drag coefficient, CL0The lift coefficient of the cylinder is fixed.
In some preferred embodiments, the boundary conditions during pipelaying are:
r(0,t)=r(L,t)=0 (15)
wherein L is the length of the riser, vxIs the pipe laying speed in the downstream direction x.
In some preferred embodiments, the initial conditions are:
r(z,0)=0 (17)
p(z,0)=q(z,0)=2 (19)
wherein t is 0, and z is more than 0 and less than L.
In some preferred embodiments, the solving the model comprises: and obtaining the vibration amplitude, the vibration frequency and the vibration mode.
In a second aspect, the present application provides a computer readable storage medium having stored therein program instructions which, when executed by a processor of a computer, cause the processor to carry out the above-mentioned method.
Compared with the prior art, the invention has the following beneficial effects:
the method comprises the steps of establishing a model for the flexible vertical pipe in the pipe laying process to obtain a three-dimensional coupled structure motion equation and a wake vortex oscillator equation, and setting boundary conditions to simulate the dynamic behavior of the lower vertical pipe, so that the method can be applied to the condition of the lower vertical pipe; the flow field around the cylinder does not need to be calculated, so that the calculation speed can be improved; and (3) carrying out numerical solution on the structural motion equation and the wake vortex oscillator equation based on the boundary condition and the initial condition so as to forecast the vortex-induced vibration of the lower vertical pipe, and the method can be widely applied to the industry.
Drawings
FIG. 1 is a schematic view of a pipe laying operation according to an embodiment of the present invention;
fig. 2 is a schematic flow chart of a method for forecasting vortex-induced vibration during pipe laying according to an embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary in nature and is not intended to limit the scope of the invention or its application.
It is to be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in an orientation or positional relationship indicated in the drawings to facilitate the description of the embodiments of the invention and to simplify the description, and are not intended to indicate or imply that the device or element so referred to must have a particular orientation, be constructed in a particular orientation, and be constructed in a particular manner of operation, and are not to be construed as limiting the invention.
The embodiment provides a method for forecasting vortex-induced vibration in a pipe laying process, in particular to a method for forecasting vortex-induced vibration in an ocean pipe laying process, which can calculate vortex-induced vibration response in a flexible pipe cable pipe laying process. The method for forecasting the vortex-induced vibration of the embodiment comprises modeling the flexible riser and solving the flexible riser model.
Step A10, modeling the flexible riser, namely establishing a model of the marine flexible riser, comprises the steps A1 to A3.
And A1, obtaining a three-dimensional coupled structure motion equation and a wake vortex oscillator equation.
The structural motion equation and the wake vortex vibrator equation are models of the marine flexible riser.
And step A2, determining the boundary condition of the model. Wherein the boundary conditions simulate the dynamic behavior of the lowering riser.
Step A3, determining the initial conditions of the model.
Step A20, solving the model: and carrying out numerical solution on a structural motion equation and a wake vortex oscillator equation based on the boundary condition and the initial condition so as to forecast vortex-induced vibration.
The present embodiment will be described in detail below.
The physical system considered in this example is a flexible beam with a velocity at the boundary, with a diameter D of the riser placed in the sea. The cylindrical deformation of the riser is calculated by the euler-bernoulli beam equation. The riser is free to vibrate in both the flow direction (x-axis) and the transverse direction (y-axis). The equation of motion control for x and y displacement along riser height at any time t >0 and location 0< z < L is expressed as:
wherein
r=x+iy (2)
F=Fx+iFy (3)
Fx=fD+f′D (4)
R=Rs+Rf=2ξdMΩs+γρD2Ωf (6)
In the above model, equation (1) is a structural motion equation. For convenience, the displacement r and the excitation force F are expressed in complex numbers, i being the imaginary unit; the displacement r can be decomposed into x (down-flow) and y (cross-flow) displacements (equation 2); the excitation force F is the fluid force exerted on the riser, resolved into FxAnd Fy(equation 3). L is the riser length. External force F in x directionxIs the average resistance fDAnd oscillation resistance fD' of (equation 4). In the model, the mass M comprises a structural mass MsAnd an additional mass (equation 5). Ca is an additional mass coefficient, considered as a constant, and its variation is ignored. Rho is the seawater density and D is the riser diameter. The damping R is decomposed into structural damping RsAnd additional damping Rf(equation 6); gamma is a constant; xi shapedIs the damping ratio. OmegafFor the vortex shedding frequency, the formula isWhere St is the Strouhal number, U is the flow rate, ΩnIs the natural frequency of the tube in air.
Due to the relatively low mass of the riser, its characteristic natural frequency ΩsWill use the natural frequency in waterRate (equation 7). On the other hand, the stiffness EI is assumed to be constant along the length of the cylinder. The tension T of the riser varies with the arc length. The method of calculating the tension T as a function of the arc length is described by taking the S-lay method as an example. Initial tension T at upper end of stinger in horizontal direction0For horizontal, balanced with the horizontal component of tension t (z), and riser gravity and buoyancy balanced with the vertical component of tension t (z), formulated as:
when the external force applied to the cylinder is estimated,is the resistance coefficient of the fixed cylinder and has the calculation formula of CD0(1+Kq2) (ii) a Wherein K is an amplification factor; cD0The average resistance coefficient of the fixed cylinder is; q is a variable related to wake vortex, and F is lift forceyIs related to the size of (a). Thus, the resistance f acting on the cylinder per unit lengthDIs calculated by the formula
Resistance to oscillation fD' (EQUATION 10) and lift Fy(equation 11) is calculated as
Wherein,
wherein C isDiIs a coefficient of resistance to oscillation, CDi0Is the amplitude of the oscillation drag coefficient, CLIs the coefficient of lift, CL0The lift coefficient of the cylinder is fixed. The lift and drag of the oscillations are periodically varying, self-limiting, satisfying Van der Pol nonlinear oscillator equations, expressed as:
equations (14-15) are the wake vortex oscillator equations. Where p is a variable related to wake vortex and f is the resistance to oscillationD' the size is related; a. thex、Ay、εxAnd εyAre empirical parameters and are determined by experimentation. The right term of equation (14-15) is the coupling of the wake vortex oscillator and the motion equation, where the coupling between the structural motion equation and the van der pol oscillator is the widely used acceleration coupling.
In the studied control equation, the structural motion equation involves the differentiation of space and time, as in equations (16-17), and the boundary conditions during the pipe laying process simulate the dynamic behavior of the lowering pipe, specifically:
r(0,t)=r(L,t)=0 (16)
wherein, assuming that the pipe laying operation is carried out in an x-z plane, the pipe laying speed is along the direction of the riser, and the boundary condition is set that the speed of the boundary at the two ends of the x is the pipe laying speed. v. ofxIs the pipe laying speed in the downstream direction x.
Initial conditions (t ═ 0) were (0 < z < L):
r(z,0)=0 (18)
p(z,0)=q(z,0)=2 (20)
assuming that at the start of vibration, the initial displacement and initial velocity are zero as in equations (18-19); the initial value of the wake vortex oscillator is 2 and the initial velocity is zero as in equations (20-21).
The model is then solved. The displacement time courses (x, y) in the forward direction and the transverse direction are obtained by numerical methods including but not limited to a difference method through simultaneous solving of equations (1, 14-15), and the vibration amplitude, the vibration frequency and the vibration mode are further analyzed.
In the embodiment, a three-dimensional coupled structure motion equation and a wake vortex oscillator equation are obtained by establishing a model for the flexible vertical pipe in the pipe laying process, and boundary conditions are set to simulate the dynamic behavior of the lower vertical pipe, so that the method can be applied to the condition of the lower vertical pipe; the method is a semi-empirical model method, wherein related empirical parameters are determined through experiments, compared with a computational fluid dynamics method, the wake vortex oscillator model method does not need to calculate a flow field around a cylinder, so that the calculation speed is high, the method can be widely applied to the industry, can provide reference for design and constructors, and can be applied to an S-shaped pipe laying method, a J-shaped pipe laying method and a pipe coiling type pipe laying method.
The method of the embodiment can be executed by a computer, and the vortex-induced vibration in the pipe laying process is forecasted by acquiring relevant parameters.
Those skilled in the art will appreciate that all or part of the processes of the embodiments methods may be performed by a computer program, which may be stored in a computer-readable storage medium and executed to perform the processes of the embodiments methods. And the aforementioned storage medium includes: various media capable of storing program codes, such as ROM or RAM, magnetic or optical disks, etc.
The foregoing is a further detailed description of the present application in connection with specific/preferred embodiments and is not intended to limit the present application to that particular description. For a person skilled in the art to which the present application pertains, several alternatives or modifications to the described embodiments may be made without departing from the concept of the present application, and these alternatives or modifications should be considered as falling within the scope of the present application.
Claims (6)
1. A method for forecasting vortex-induced vibration in a pipe laying process is characterized by comprising the steps of modeling a flexible riser and solving the model;
the modeling the flexible riser comprises:
a1, obtaining a three-dimensional coupled structure motion equation and a wake vortex oscillator equation;
a2, determining the boundary condition of the model; wherein the boundary conditions simulate dynamic behavior of the lowering riser;
a3, determining the initial condition of the model;
the solving the model comprises: numerically solving the structural motion equation and the wake vortex oscillator equation based on the boundary condition and the initial condition, thereby forecasting vortex-induced vibration;
the structural equation of motion is:
the mass M comprises a vertical pipe mass and an additional mass, R is the displacement of the vertical pipe, t is time, z is the height of the vertical pipe, R is damping, and EI is the rigidity of the vertical pipe; t is the tension of the stand pipe, and F is the exciting force;
the wake vortex oscillator equation is:
where p is a trailing vortex-related variable related to the oscillation resistance fD' is size dependent; q is a variable related to wake vortex, and F is lift forceyIs related to the size of (a); a. thex,Ay,εx,εyAs an empirical parameter, ΩfThe vortex shedding frequency is D, the diameter of the stand pipe is D, x is the displacement of the stand pipe along the forward direction, and y is the displacement of the stand pipe along the transverse direction;
r=x+iy (2)
F=Fx+iFy (3)
Fx=fD+f'D (4)
R=Rs+Rf=2ξdMΩs+γρD2Ωf (6)
the displacement r and the exciting force F are expressed by complex numbers, i is an imaginary unit; the displacement r is decomposed into displacement in the forward flow direction x and the transverse flow direction y; the excitation force F is the fluid force exerted on the riser and can be decomposed into FxAnd Fy(ii) a External force F in x-directionxIs the average resistance fDAnd oscillation resistance fD' sum of; the mass M comprises a structural mass MsAnd an additional mass; ca is an additional mass coefficient, considered as a constant, the variation of which is ignored; rho is the density of the seawater; d is the diameter of the stand pipe; the damping R is decomposed into structural damping RsAnd an additional resistorNiRf(ii) a Gamma is a constant; xi shapedIs the damping ratio; omegafFor vortex shedding frequency, ΩfHas a calculation formula of omegaf2 pi StU/D, where St is Strouhal number, U is flow rate, ΩnThe natural vibration circle frequency of the vertical pipe in the air; characteristic natural frequency omega of the risersAdopting natural frequency in water; the stiffness EI is assumed to be constant along the length of the riser cylinder; the tension T varies with arc length.
2. The method of claim 1, wherein: when calculating the external force applied to the vertical pipe cylinder, the resistance coefficient of the fixed cylinderIs calculated by the formula CD0(1+Kq2) (ii) a K is an amplification factor; cD0The average resistance coefficient of the fixed cylinder is; q is a variable related to wake vortexes and is related to the magnitude of lift force; resistance force f acting on cylinder per unit lengthDThe calculation formula of (2) is as follows:
resistance to oscillation fD' and lift force FyThe calculation formula of (2) is as follows:
wherein, the oscillation resistance coefficient CDiAnd coefficient of lift CLThe calculation formula of (2) is as follows:
wherein, CDi0Is the amplitude of the oscillation drag coefficient, CL0Is a fixed cylindrical lift coefficient.
3. The method of claim 1, wherein the boundary conditions during pipelaying are:
r(0,t)=r(L,t)=0 (15)
5. The method of claim 1, wherein solving the model comprises: and obtaining the vibration amplitude, the vibration frequency and the vibration mode.
6. A computer-readable storage medium, comprising: the computer-readable storage medium has stored therein program instructions which, when executed by a processor of a computer, cause the processor to carry out the method according to any one of claims 1 to 5.
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