A method for calculating vortex-induced vibration of a deep-sea mining riser under internal wave action

Abstract

The application belongs to the technical field of marine resource development, and is a calculation method for vortex-induced vibration of a deep-sea mining riser under the action of internal waves. According to wave parameters such as the wave amplitude and wavelength of the marine internal waves, the velocity and acceleration distribution characteristics of the flow field are determined to provide load input for the calculation of vortex-induced vibration of the deep-sea mining riser. The marine internal wave flow field has significant particularity, which is different from uniform flow and typical shear flow, and is a kind of non-uniform shear flow. Based on the particularity of the marine internal wave flow field, the vortex-induced load distribution on the deep-sea mining riser under the action of the improved traditional wake oscillator model is obtained. In view of the geometric nonlinearity problem caused by the large slenderness ratio of the deep-sea mining super-long riser and the weak constraint characteristics of the deep-sea mining riser, the rigid body displacement and elastic deformation of the riser are separated and calculated by using the co-rotational coordinate method, so as to improve the calculation efficiency to meet the actual engineering requirements, and form the calculation method for vortex-induced vibration of the deep-sea mining riser under the action of the marine internal waves.

Description

Technical Field

[0001] This invention relates to the field of marine resource development technology, and in particular to a method for calculating vortex-induced vibration of deep-sea mining risers under internal wave action. Background Technology

[0002] Polymetallic nodules and cobalt-rich crusts in seabed mineral deposits are important strategic resources, providing essential raw materials for industries such as energy, aerospace, and electronics. Deep-sea mining equipment is crucial in the development of deep-sea mineral resources. Deep-sea mineral transport pipelines, in particular, are subjected to complex marine environmental loads during long-term offshore operations. Accurate prediction of the vortex-induced vibration response of marine risers is a key guarantee and important support for safe operation and production in deep-sea mining engineering.

[0003] Currently, the computational accuracy for ultra-long, geometrically nonlinear pipelines used in deep-sea mining is insufficient to meet the demands of practical engineering and timeliness. Therefore, developing a method for predicting the dynamic response of risers under complex marine environmental loads with independent intellectual property rights has significant engineering value and scientific importance. Surface waves and ocean currents are typical marine environmental loads experienced by marine risers, but the frequent occurrence of internal ocean waves has attracted increasing attention from scholars and engineers. Internal ocean waves, due to their characteristics of being hidden underwater, having a large scale, and exhibiting strong nonlinearity, are significantly different from surface waves, making their dynamic characteristics on marine risers more complex. Furthermore, marine risers possess large aspect ratios and strong geometrical nonlinearity, thus posing a challenge to the development of numerical simulation methods for the effects of internal ocean wave loads on marine risers under real-scale conditions.

[0004] Unlike typical uniform and shear flow fields, the flow field around risers in deep-sea mining exhibits unsteady and strong shear characteristics as internal ocean waves propagate. Therefore, commonly used wake oscillator models for assessing vortex-induced loads are insufficient to accurately predict the vortex-induced loads on risers under the influence of internal waves. It is necessary to modify and improve the wake oscillator model based on the specific characteristics of the internal wave flow field to enhance the accuracy of riser vortex-induced load assessment. This, in turn, provides accurate internal solitary wave load input for the riser, enabling real-time and accurate calculation of the riser's vortex-induced vibration response. The large aspect ratio and strong geometric nonlinearity of full-scale marine risers pose challenges to the efficient and accurate solution of their dynamic response. Furthermore, for weakly constrained marine risers in deep-sea mining hydraulic lifting systems, the large deformation typical of risers, coupled with significant rigid body displacements, under marine environmental loads further increases the workload of iterative calculations in the finite element model, thereby reducing the computational efficiency of the riser's dynamic response. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for calculating the vortex-induced vibration of deep-sea mining risers under internal wave loading. Based on the unsteady strong shear characteristics of the ocean internal wave flow field and considering the instantaneous characteristics of vortex shearing, this invention improves the wake oscillator model to determine the vortex-induced load on deep-sea mining risers under internal wave loading. Furthermore, this invention uses an efficient co-rotating coordinate beam element finite element method to solve the vortex-induced vibration response of a real-scale marine riser under the action of an internal solitary wave flow field, thereby enabling the prediction and analysis of the vortex-induced vibration response of deep-sea mineral transport risers under the influence of ocean internal wave loading, providing a basis for the engineering design of deep-sea mining risers.

[0006] The technical means employed in this invention are as follows:

[0007] A method for calculating vortex-induced vibration of deep-sea mining risers under internal wave action, comprising:

[0008] Unsteady time-domain distribution information of flow field velocity is obtained based on ocean internal wave parameters;

[0009] Based on the unsteady time-domain distribution information of the flow field velocity, the vortex shedding frequency in the oscillator equation is modified to obtain a wake oscillator model that considers instantaneous changes.

[0010] Based on the wake oscillator model, the vortex-induced load distribution on the deep-sea mining riser in the ocean internal wave field at different times was obtained.

[0011] To address the strong geometric nonlinearity of deep-sea mining risers, control equations and constitutive relations suitable for dynamic response analysis of deep-sea mining risers are constructed.

[0012] Based on the beam element model and co-rotating coordinate system, the control equations are discretized using the finite element method to establish a numerical model of the dynamic response of a deep-sea mining riser.

[0013] Using the aforementioned dynamic response numerical model, the vortex-induced vibration response of the deep-sea mining ultra-long riser is calculated based on the vortex-induced load distribution on the riser.

[0014] Update the time step and repeatedly calculate the vortex-induced vibration response at different times until the preset time calculation is completed to obtain the time-domain response characteristics of the deep-sea mining riser.

[0015] Furthermore, the acquisition of unsteady time-domain distribution information of flow field velocity based on ocean internal wave parameters specifically includes:

[0016] Based on the actual wave parameters of internal ocean waves, the velocity distributions of the upper and lower layers of the stratified fluid system are obtained using layer-averaged theory:

[0017]

[0018] Where u1(x,t) is the upper fluid velocity; u2(x,t) is the lower fluid velocity; η(x,t) is the position of the inner wave surface; x is the horizontal coordinate; t is time; h1 is the upper fluid depth; h2 is the upper fluid depth; c is the phase velocity of the inner wave; ρ1 is the upper fluid density; ρ2 is the density of both the upper and lower fluids; ρ0 is the average density of the fluid system; and g is the gravitational acceleration.

[0019] Furthermore, the wake oscillator model considering instantaneous changes specifically includes:

[0020] The steady fluid velocity in the wake oscillator model is replaced with a time-varying velocity profile induced by ocean internal waves to obtain instantaneous information of the flow field around the deep-sea mining riser; considering the influence of density stratification, the eddy Strouhal number St(z,t) in the stratified fluid is introduced:

[0021] St(z,t)=St0(z,t)f(Ri(z))

[0022]

[0023] Where St0(z,t) is the uniform density eddy Strouhal number, f is the density stratification function, z is the vertical coordinate, U(z,t) represents the velocity of the ocean internal wave flow field, Ri(z) is the Richardson number in the stratified fluid, σ(z,t) is the flow field density distribution, and ρ0 is the average flow field density.

[0024] The corrected vortex shedding frequency Ω is obtained based on the improved Strauhall number. f :

[0025]

[0026] Where U(z,t) is the velocity of the internal ocean wave field; D is the outer diameter of the deep-sea mining riser.

[0027] The lift coefficient of a deep-sea mining riser caused by eddy-induced load in an internal ocean current field is obtained using the van der Pol equation:

[0028]

[0029] Where q represents the lateral lift coefficient; ε represents the equation parameter, Ω f denoted as vortex shedding frequency; F is the fluid load.

[0030] Furthermore, the method for obtaining the vortex-induced load distribution on the deep-sea mining riser includes:

[0031] By using ocean internal waves with different initial parameters and based on the wake oscillator model, the vortex shedding frequency near the deep-sea mining conveyor riser in internal wave fields of different scales and the lift coefficient of the riser in internal wave fields with different parameters are obtained, thus obtaining the distribution characteristics of vortex-induced loads along the riser.

[0032] Furthermore, the governing equations and constitutive relations for the dynamic response analysis of the deep-sea mining riser specifically include:

[0033] Introducing the Green-Lagrange strain tensor e:

[0034]

[0035] Where u represents horizontal deformation, v represents lateral deformation, and w represents vertical deformation;

[0036] The formula for calculating instantaneous tension is:

[0037] T(x,t)=T0+EA·e(x,t)

[0038] Where T0 is the initial tension of the deep-sea mining riser, EA is the axial stiffness of the deep-sea mining riser, and e(x,t) is the dynamic strain tensor of the deep-sea mining riser.

[0039] Using Euler-Bernoulli beam theory and the Updated Lagrangian scheme to track large deformations, the governing equations are obtained:

[0040]

[0041] Where r is the spatial position vector of the deep-sea mining riser, s is the arc length coordinate; A is the cross-sectional area of ​​the pipeline, EI is the elastic stiffness of the pipeline, and F is the pipeline load.

[0042] Furthermore, the numerical model of the dynamic response of the deep-sea mining riser specifically includes:

[0043] A beam element model based on a co-rotation coordinate system is used to achieve separate solutions for rigid body displacement and elastic deformation:

[0044] r = r rigid +r flex

[0045] Where, r rigid Let r be the rigid body displacement of the pipe element. flex This refers to the elastic deformation of the pipe unit.

[0046] Set the global coordinate system X i With co-rotation coordinate system The relationship is represented as:

[0047]

[0048] Where R is the rotation matrix; X0 is the origin of the co-rotation coordinate system;

[0049] The element dynamics equations in a co-rotating coordinate system are expressed as:

[0050]

[0051] Among them, M e Let C represent the mass matrix in the co-rotating coordinate system. e K represents the damping matrix in the co-rotation coordinate system. e This represents the stiffness matrix in a corotating coordinate system. This represents the element acceleration in a co-rotating coordinate system. Represents the velocity in a co-rotating coordinate system. This represents the deformed coordinates in the corotating coordinate system.

[0052] Furthermore, the calculation method for the vortex-induced vibration response of the ultra-long riser in deep-sea mining specifically includes:

[0053] A numerical model of the dynamic response of a deep-sea mining riser is used, with the vortex-induced load distribution on the riser as input, to calculate the vortex-induced vibration response of the riser. The element dynamic equations are refined, and the Newmark-β method is used to solve the numerical results, obtaining the vortex-induced vibration response of the deep-sea mining riser at different times.

[0054]

[0055] Where, m r The mass of the riser unit is represented by m. f The mass m represents the fluid inside the unit. a The additional mass of the unit is represented by C; C is the damping of the riser.

[0056] The effective tension T of the unit e Represented as:

[0057] T e =T+ρ e A e dz-(m r +m f gdz

[0058] Where, ρ e A represents the external fluid density. e This indicates the outer cross-sectional area of ​​the pipe.

[0059] Furthermore, the time-domain response characteristics of the vortex-induced vibration of the deep-sea mining riser are obtained, specifically including:

[0060] The time step is updated by repeatedly solving the vortex-induced vibration response of the deep-sea mining riser at different times to obtain the vortex-induced vibration response of each unit of the deep-sea mining riser at each time until the calculation of the specified time is completed, and the time-domain response characteristics of the vortex-induced vibration of the deep-sea mining riser are obtained.

[0061] Compared with the prior art, the present invention has the following advantages:

[0062] This invention provides a method for calculating vortex-induced vibration of deep-sea mining risers under internal wave action. By improving the wake oscillator model, it proposes an evaluation method suitable for solving the vortex-induced load of deep-sea mining and transportation pipelines under the action of internal wave flow fields. This method can obtain the instantaneous vortex-induced load of the unsteady internal wave flow field, providing load input for calculating the vortex-induced vibration response. Considering the geometric characteristics of ultra-long deep-sea mining and transportation pipelines, the axial strain of the pipeline is taken into account, and an improved strain tensor is introduced. Based on the flow field load characteristics, geometric dimensions, and material properties of the pipeline, the tension of the pipeline is corrected to obtain the effective tension of the element. In the calculation of vortex-induced vibration load, the characteristics of large aspect ratio and strong geometric nonlinearity of real-scale marine risers, as well as the special property of large rigid body displacement in weakly constrained deep-sea mineral transportation risers, are fully considered. A dynamic response calculation model based on a beam element finite element model in a co-rotating coordinate system is established, which can efficiently calculate the vortex-induced vibration response of deep-sea mineral transportation pipelines under the action of internal wave flow fields.

[0063] Based on the above reasons, this invention can be widely promoted in fields such as marine resource development. Attached Figure Description

[0064] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0065] Figure 1 This is a block diagram of the calculation method for vortex-induced vibration of deep-sea mining risers under the action of internal waves, as presented in this invention.

[0066] Figure 2 This is a schematic diagram illustrating the effect of internal waves on deep-sea mining risers in an application scenario of this invention.

[0067] Figure 3 This is a schematic diagram of the solution using the coaxial coordinate beam element method of this invention.

[0068] Figure 4 This is a deformation characteristic diagram of a deep-sea mining riser under the action of internal waves in an embodiment of the present invention. Detailed Implementation

[0069] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0070] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0072] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0073] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention. The directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0074] For ease of description, spatial relative terms such as "above," "over," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation besides the orientation of the device as described in the figures. For example, if the device in the figures is inverted, a device described as "above" or "above" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0075] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0076] like Figure 1 As shown, this invention provides a method for calculating vortex-induced vibration of deep-sea mining risers under internal wave action, including:

[0077] Obtaining the unsteady time-domain distribution information of flow field velocity based on ocean internal wave parameters; specifically, as a preferred embodiment of the present invention, obtaining the unsteady time-domain distribution information of flow field velocity based on ocean internal wave parameters specifically includes: obtaining the velocity distribution of the upper and lower regions of the stratified fluid system based on layer averaging theory according to the actual ocean internal wave parameters.

[0078]

[0079] Where u1(x,t) is the upper fluid velocity; u2(x,t) is the lower fluid velocity; η(x,t) is the position of the inner wave surface; x is the horizontal coordinate; t is the time; h1 is the upper fluid depth; h2 is the upper fluid depth; c is the phase velocity of the inner wave; ρ1 is the upper fluid density; ρ2 is the density of both the upper and lower fluids; ρ0 is the average density of the fluid system; and g is the gravitational acceleration.

[0080] Based on the unsteady time-domain distribution information of the flow field velocity, the vortex shedding frequency in the oscillator equation is modified to obtain a wake oscillator model considering instantaneous changes. Specifically, in a preferred embodiment of this invention, the wake oscillator model considering instantaneous changes includes: the unsteady and strong shear characteristics of the ocean internal wave flow field cause the flow field parameters (such as flow velocity and vortex shedding frequency) around the riser to change with time and depth. The steady fluid velocity in the wake oscillator model is replaced with a time-varying velocity profile induced by ocean internal waves to obtain instantaneous information of the flow field around the deep-sea mining riser; considering the influence of density stratification, the vortex shedding Strouhal number St(z,t) in the stratified fluid is introduced.

[0081] St(z,t)=St0(z,t)f(Ri(z))

[0082]

[0083] Where St0(z,t) is the uniform density eddy Strouhal number, f is the density stratification function, z is the vertical coordinate, U(z,t) represents the velocity of the ocean internal wave flow field, Ri(z) is the Richardson number in the stratified fluid, ρ(z,t) is the flow field density distribution, and ρ0 is the average flow field density.

[0084] The corrected vortex shedding frequency Ω is obtained based on the improved Strauhall number. f :

[0085]

[0086] Where U(z,t) is the velocity of the internal ocean wave field; D is the outer diameter of the deep-sea mining riser.

[0087] The lift coefficient of a deep-sea mining riser caused by eddy-induced load in an internal ocean current field is obtained using the van der Pol equation:

[0088]

[0089] Where q represents the lateral lift coefficient; ε represents the equation parameter, Ω f Let Ω be the vortex shedding frequency; F be the fluid load. Compared to the traditional van der Pol equation, this equation shows a different vortex shedding frequency Ω. f The instantaneous frequency is used, which characterizes the difference and improvement of the internal wave flow field compared with other typical flow fields.

[0090] Based on the aforementioned wake oscillator model, the vortex-induced load distribution on the deep-sea mining riser in the ocean internal wave current field at different times is obtained; specifically, as a preferred embodiment of the present invention, the method for obtaining the vortex-induced load distribution on the deep-sea mining riser includes:

[0091] By using ocean internal waves with different initial parameters and based on a wake oscillator model, the vortex shedding frequency near the deep-sea mining riser in internal wave fields of different scales and the lift coefficient of the riser in internal wave fields with different parameters are obtained, thus revealing the distribution characteristics of vortex-induced loads along the riser. Based on the obtained temporal distribution characteristics of vortex-induced loads in the deep-sea mining riser, load input is provided for the calculation of vortex-induced vibration of the riser.

[0092] To address the strong geometric nonlinear characteristics of deep-sea mining risers, a governing equation and constitutive relation suitable for dynamic response analysis of deep-sea mining risers are constructed. Specifically, in a preferred embodiment of this invention, the governing equation and constitutive relation for the dynamic response analysis of deep-sea mining risers include: considering the strong geometric nonlinear characteristics of ultra-long deep-sea mining risers, lateral vibration leads to an increase in the actual arc length of the riser, inducing additional axial strain; therefore, a Green-Lagrange strain tensor e is introduced:

[0093]

[0094] Where u represents horizontal deformation, v represents lateral deformation, and w represents vertical deformation;

[0095] Extra-long risers are typically subjected to initial tension applied by a top tensioner or buoyancy module, but ocean internal wave loads cause the tension to be time-varying. The formula for calculating the instantaneous tension is:

[0096] T(x,t)=T0+EA·e(x,t)

[0097] Where T0 is the initial tension of the deep-sea mining riser, EA is the axial stiffness of the deep-sea mining riser, and e(x,t) is the dynamic strain tensor of the deep-sea mining riser.

[0098] Using Euler-Bernoulli beam theory and the Updated Lagrangian scheme to track large deformations, the governing equations are obtained:

[0099]

[0100] Where r is the spatial position vector of the deep-sea mining riser, s is the arc length coordinate; A is the cross-sectional area of ​​the pipeline, EI is the elastic stiffness of the pipeline, and F is the pipeline load.

[0101] Based on the beam element model and co-rotating coordinate system, the finite element method is used to discretize the governing equations, and a numerical model of the dynamic response of a deep-sea mining riser is established; for example... Figure 3As shown. In a specific implementation, as a preferred embodiment of the present invention, the numerical model of the dynamic response of the deep-sea mining riser specifically includes: considering the typical characteristics of large length-to-slenderness ratio and weak constraints of ultra-long deep-sea mining transport pipelines, a beam element model based on a co-rotating coordinate system is adopted to achieve separate solutions for rigid body displacement and elastic deformation, which can greatly reduce the number of iterations and improve the computational efficiency of the dynamic response of the real-scale riser.

[0102] r = r rigid +r flex

[0103] Where, r rigid Let r be the rigid body displacement of the pipe element. flex This refers to the elastic deformation of the pipe unit.

[0104] Set the global coordinate system X i With co-rotation coordinate system The relationship is represented as:

[0105]

[0106] Where R is the rotation matrix; X0 is the origin of the co-rotation coordinate system;

[0107] The element dynamics equations in a co-rotating coordinate system are expressed as:

[0108]

[0109] Among them, M e Let C represent the mass matrix in the co-rotating coordinate system. e K represents the damping matrix in the co-rotation coordinate system. e This represents the stiffness matrix in a corotating coordinate system. This represents the element acceleration in a co-rotating coordinate system. Represents the velocity in a co-rotating coordinate system. This represents the deformed coordinates in the corotating coordinate system.

[0110] Using the aforementioned dynamic response numerical model, the vortex-induced vibration response of the ultra-long deep-sea mining riser is calculated based on the vortex-induced load distribution on the riser. Specifically, as a preferred embodiment of the invention, the calculation method for the vortex-induced vibration response of the ultra-long deep-sea mining riser includes: using the dynamic response numerical model of the deep-sea mining riser, taking the vortex-induced load distribution on the riser as input, and calculating the vortex-induced vibration response of the riser; refining the element dynamic equations, and solving the numerical values ​​using the Newmark-β method to obtain the vortex-induced vibration response of the riser at different times.

[0111]

[0112] Where, mr The mass of the riser unit is represented by m. f The mass m represents the fluid inside the unit. a The additional mass of the unit is represented by C; C is the damping of the riser.

[0113] The effective tension T of the unit e Represented as:

[0114] T e =T+ρ e A e dz-(m r +m f gdz

[0115] Where, ρ e A represents the external fluid density. e This indicates the outer cross-sectional area of ​​the pipe.

[0116] The time step is updated, and the vortex-induced vibration response at different times is repeatedly calculated until the preset time calculation is completed, thereby obtaining the time-domain response characteristics of the vortex-induced vibration of the deep-sea mining riser. Specifically, in a preferred embodiment of the present invention, obtaining the time-domain response characteristics of the vortex-induced vibration of the deep-sea mining riser specifically includes: updating the time step, and repeatedly solving for the vortex-induced vibration response of the deep-sea mining riser at different times to obtain the vortex-induced vibration response of each unit of the deep-sea mining riser at each time, until the calculation for the specified time is completed, thereby obtaining the time-domain response characteristics of the vortex-induced vibration of the deep-sea mining riser.

[0117] Example

[0118] like Figure 1 As shown, this invention provides a method for calculating vortex-induced vibration of deep-sea mining risers under internal wave action. The application scenarios of this invention are as follows: Figure 2 As shown, this embodiment uses the calculation of the dynamic vortex-induced vibration response of a deep-sea mining riser under the action of ocean internal waves as an example to illustrate the specific implementation method of the present invention.

[0119] In this embodiment, the internal wave height is selected as 50m, and the waveform η(x,t) of the internal solitary wave is given by nonlinear MCC theory. The upper water depth h1 is taken as 50m, the lower water depth h2 is taken as 250m, and the trough of the internal solitary wave is located at a distance of 500m from the riser. Based on the distance of the internal solitary wave from the riser and its propagation speed, the action time is set to 1000s to ensure that the wave surface of the internal solitary wave can completely pass through the riser. The calculated operating parameters are shown in Table 1.

[0120] The velocity distributions in the upper and lower regions of a layered fluid system are obtained based on layer-averaged theory:

[0121]

[0122] X = xcMCC t

[0123]

[0124] ζ1=h1-η2

[0125] ζ2=h2-η2

[0126] Table 1. Operating parameters of internal wave action on deep-sea mining riser.

[0127] parameter Value Total pipe length L / m 300 Pipe outer diameter D / m 0.25 Pipe inner diameter d / m 0.2 Pipe material density p r / kg·m -3 ]]> 7850 Pipe elastic modulus E / GPa 210 Internal wave amplitude a / m 50 <![CDATA[Upper water depth h1 / m]]> 50 <![CDATA[Depth of the lower layer water h2 / m]]> 250 <![CDATA[Upper layer density ρ1 / kg·m -3 > 1000 <![CDATA[Lower layer density ρ2 / kg·m -3 > 1025

[0128] Deformation characteristics of deep-sea mining risers under internal wave action, such as Figure 4 As shown. By solving the vortex-induced vibration response of the deep-sea mining riser, the vortex-induced vibration response of each unit of the deep-sea mining riser at that moment is obtained. The time step is updated and the previous calculation steps are repeated to obtain the vortex-induced vibration response of the deep-sea mining riser under the action of the internal wave flow field at the next moment, until the calculation is completed for a specified time, and the time-domain response characteristics of the vortex-induced vibration of the deep-sea mining riser are obtained.

[0129] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating vortex-induced vibration of a deep-sea mining riser under internal wave action, characterized in that, The method comprises the following steps: obtaining non-steady time domain distribution information of flow field velocity based on ocean internal wave parameter; modifying vortex shedding frequency in a vortex equation based on the non-steady time domain distribution information of flow field velocity, and obtaining a wake vortex model considering instantaneous change; the wake vortex model considering instantaneous change specifically comprises: The steady fluid velocity in the wake vortex model is replaced by the time-varying velocity profile induced by the internal wave in the ocean, and the instantaneous information of the flow field around the deep-sea mining riser is obtained; considering the influence of the density jump layer, the vortex de-strouhal number in the stratified fluid is introduced : where is the homogeneous density vortex Strouhal number, is the density stratification function, is the vertical coordinate, denotes the oceanic internal wave field velocity, is the Richardson number in the stratified fluid; is the flow field density distribution; is the flow field average density; Modified vortex shedding frequency from improved strouhal number : wherein, D is the outer diameter of the deep sea mining riser; obtaining lift coefficient caused by vortex-induced load of a deep-sea mining riser in an ocean internal wave flow field through a van der Pol equation: wherein, represents the lateral lift coefficient; represents the equation parameter, is the fluid load; obtaining vortex-induced load distribution on the deep-sea mining riser in the ocean internal wave flow field at different time instants based on the wake vortex model; constructing control equations and constitutive relations suitable for dynamic response analysis of the deep-sea mining riser in view of strong geometric nonlinearity of the deep-sea mining riser; discretizing the control equations by using a finite element method based on a beam element model and a co-rotational coordinate system, and establishing a dynamic response numerical model of the deep-sea mining riser; calculating vortex-induced vibration response of the deep-sea mining riser according to the vortex-induced load distribution on the deep-sea mining riser by using the dynamic response numerical model; updating a time step, and repeatedly calculating vortex-induced vibration response at different time instants until a preset time calculation is completed, and obtaining vortex-induced vibration time domain response characteristics of the deep-sea mining riser.

2. The method of claim 1, wherein, The method for obtaining non-steady time domain distribution information of flow field velocity based on ocean internal wave parameter specifically comprises: obtaining velocity distribution of an upper region and a lower region of a layered fluid system based on a layer-averaged theory according to wave parameters of an actual ocean internal wave; wherein, is the upper fluid velocity; is the lower fluid velocity; is the internal wave surface position; is the horizontal coordinate, is time, is the upper fluid depth, is the upper fluid depth; is the phase velocity of the internal wave; is the upper fluid density, is the upper and lower fluid density; is the gravitational acceleration.

3. The method of claim 1, wherein, the method for obtaining vortex-induced load distribution on the deep-sea mining riser specifically comprises: obtaining vortex shedding frequency near the deep-sea mining riser in an internal wave flow field of different scales and lift coefficient of the riser in an internal wave flow field of different parameters based on the wake vortex model by giving ocean internal waves of different initial parameters, and obtaining distribution characteristics of vortex-induced load along the riser.

4. The method of claim 1, wherein, The control equations and constitutive relations for dynamic response analysis of the deep-sea mining riser specifically comprise: Introducing the Green-Lagrange strain tensor : wherein is the horizontal deformation, is the lateral deformation, is the vertical deformation; a calculation formula of instantaneous tension is: wherein, is the initial tension of the deep-sea mining riser, is the axial stiffness of the deep-sea mining riser; is the dynamic strain tensor of the deep-sea mining riser; obtaining control equations by using Euler-Bernoulli beam theory combined with an Updated Lagrangian format for tracking large deformation: wherein, is the spatial position vector of the deep-sea mining riser, is the arc length coordinate; is the cross-sectional area of the pipe, is the elastic stiffness of the pipe, and f is the pipe load.

5. The method of claim 4, wherein, The dynamic response numerical model of the deep-sea mining riser specifically comprises: separately solving rigid body displacement and elastic deformation by using a beam element model based on a co-rotational coordinate system: wherein, is the rigid body displacement of the pipe unit, is the elastic deformation of the pipe unit; The relationship between the global coordinate system and the co-rotational coordinate system is expressed as: wherein is a rotation matrix; is the origin of the co-rotational coordinate system; expressing an element dynamics equation in the co-rotational coordinate system as: wherein, M represents a mass matrix in the co-rotational coordinate system, C represents a damping matrix in the co-rotational coordinate system, K represents a stiffness matrix in the co-rotational coordinate system; a represents an element acceleration in the co-rotational coordinate system, v represents a velocity in the co-rotational coordinate system, ε represents a deformation coordinate in the co-rotational coordinate system.

6. The method of calculating vortex-induced vibration of a deep-sea mining riser under internal wave action according to claim 5, wherein, The method for calculating vortex-induced vibration response of the deep-sea mining riser specifically comprises: calculating vortex-induced vibration response of the deep-sea mining riser by taking vortex-induced load distribution on the deep-sea mining riser as input by using the dynamic response numerical model of the deep-sea mining riser, and solving the element dynamics equation by using a Newmark-β method to obtain vortex-induced vibration response of the deep-sea mining riser at different time instants: wherein, represents the added mass of the unit; is the damping of the riser; effective tension of the cell is represented as: wherein, represents the density of the external fluid, represents the outer cross-sectional area of the pipe.

7. The method of claim 1, wherein, obtaining vortex-induced vibration time domain response characteristics of the deep-sea mining riser specifically comprises: updating a time step, and obtaining vortex-induced vibration response of each element of the deep-sea mining riser at each time instant by repeatedly solving vortex-induced vibration response of the deep-sea mining riser at different time instants until a calculation of a specified time is completed, and obtaining vortex-induced vibration time domain response characteristics of the deep-sea mining riser.

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