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Multi-field coupling multiple nonlinear vibration model and fatigue failure mechanism of deep-ocean mining hydraulic lifting pipe

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Abstract

In deep-ocean mining operation, the fatigue life of lifting pipe has always been the focus of field operators, and the fatigue failure mechanism has attracted more and more attention of scholars, but it has not been effectively disclosed. Therefore, in this work, a multi-field coupling and multiple nonlinear vibration model of lifting pipe is established, which can accurately determine the alternating stress of deep-ocean lifting pipe. The nonlinear fatigue damage prediction method of lifting pipe based on load interaction effect and residual strength attenuation degradation is established using Corten–Dolan cumulative damage method, which can accurately determine the fatigue life of deep-ocean lifting pipe. Finally, the influences of outflow velocity, buffer station masses and internal flow velocity on the fatigue life of lifting pipe are analyzed. It is found that, firstly, with the increase in the outflow velocity, the fatigue life of the pipe tends to decrease first and then increase, and an external flow rate with the maximum fatigue life appears. However, in real operation, the external flow rate cannot be controlled. Therefore, according to a certain external flow rate, the optimal structure setting can be evaluated by the analysis method established. Secondly, with the increase in the buffer station mass, the fatigue life of the lifting pipe tends to decrease first and then increase. There is an optimal buffer station mass configuration parameter on the site, which is related to the riser structure, ocean flow velocity, internal flow velocity and can be determined by the analysis methodology. Thirdly, with the increase in the lifting flow rate, the fatigue life of the lifting pipe tends to increase first and then decrease. Therefore, when determining to configure the lifting flow rate on-site, it is necessary to use the proposed nonlinear fatigue damage analysis methodology to analyze whether it is in a dangerous state. If it does not meet the site requirements, other parameters can be set, to improve the fatigue life of the lifting pipe.

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The data used to support the findings of this study are included within the article.

Abbreviations

VIV:

Vortex-induced vibration

CF:

Cross flow

RMS:

Root mean square

CFD:

Computational fluid dynamics

IL:

In-line

3D:

Three-dimensional

\(u_{1} \left( {z,t} \right)\) :

Displacement field function corresponding to coordinate system \(x\)

\(u_{3} \left( {z,t} \right)\) :

Displacement field function corresponding to coordinate system \(z\)

\(\upsilon_{y} \left( {z,t} \right)\) :

CF displacement of lifting pipe

\(E\) :

Elastic modulus of the lifting pipe material

\(L\) :

Length of the lifting pipe unit

\(\upsilon^{\prime\prime}_{i} ,i = x,y,z\) :

Second derivative of the lifting pipe displacements with respect to z

\(v_{x}\), \(v_{y}\), \(v_{z}\) :

Absolute velocities of the internal fluid in the x-, y- and z-directions

\(\rho_{{\text{i}}}\) :

Internal fluid density

\(\dot{\upsilon }_{i} ,i = x,y,z\) :

First-order derivative of the lifting pipe displacement with respect to time for the x-, y- and z-directions

\(U\) :

Multiphase flow velocity in the lifting pipe unit

\(F_{{\text{L}}} \left( {z,t} \right)\) :

Lateral lift in the CF direction

\(f_{y} \left( {z,t} \right)\) :

High-speed fluid impact loads in the lifting pipe in the y-directions

\(F_{x} \left( {z,t} \right)\) :

Longitudinal force of the lifting pipe

\(\alpha_{1} \left( t \right)\) :

Deflection angles of the upper micro-segments in the x-directions

\(\varphi_{1} \left( t \right)\) :

Deflection angles of the lower micro-segments in the y-directions

\(\zeta\) :

Damping ratio

\(D_{{\text{o}}}\) :

Outer diameter of the lifting pipe

\(f\) :

Friction coefficient caused by fluid viscosity

\(c\) :

Damping coefficient

\(M_{C}\) :

Mass of the buffer station

\(\overline{C}_{{\text{d}}}\), \(\overline{C}_{{\text{l}}}\) :

Steady-state drag force coefficient and lift force coefficient

\(q_{x} ,q_{y}\) :

Dimensionless wake oscillator variables in the IL flow direction and CF direction

\(S_{t}\) :

Strouhal coefficient

\(d_{p}\) :

Element generalized force matrix

\(C_{{\text{p}}}\) :

Particle drag force coefficient

\(P\) :

Internal pressure

\(\tau_{i}\) :

Fluid viscous shear stress

\(\lambda_{m}\) :

Wall friction coefficient

\(B_{1}\), \(B_{2}\) :

Heave radiation and heave viscous damping

\(\eta \left( t \right)\) :

Surface displacements of the random wave

\(\hat{\omega }_{i}\) :

Circular frequency of the \(i\)-th harmonic

\(M\) :

Interval number of the partition

\(\Delta \omega\) :

Frequency step

\(\overline{f}\) :

The frequency

\(H_{1/3}\) :

Significant wave height

\(f_{{\text{p}}}\) :

Peak frequency

\(\gamma\) :

Peak parameter

\(R\) :

Platform radius

\(d\) :

Draft of the platform

\(B_{{{\text{plate}}}}^{{}}\) :

Width of the heave plate

\(p\) :

Number of damage nuclei under stress

\(a\) :

Constant related to the material

\(p_{{{\text{max}}}}\) :

Number of damage nuclei

\(a_{\max }\) :

Material constant

\(p_{i}\) :

Number of damage nuclei

\(a_{i}\) :

Material constant

\(N_{{\text{f}}}\) :

Fatigue life under multistage stress cycle

\(\sigma_{i}\) :

The \(i\) stress

\(d\) :

Parameter related to material properties

\(R\left( n \right)\) :

Material residual strength

\(A_{i}\) :

Strength degradation coefficient

\(u_{2} \left( {z,t} \right)\) :

Displacement field function corresponding to coordinate system \(y\)

\(\upsilon_{x} \left( {z,t} \right)\) :

IL displacement of lifting pipe

\(\upsilon_{z} \left( {z,t} \right)\) :

Longitudinal displacement of lifting pipe

\(A\) :

Cross-sectional area of the lifting pipe

\(\upsilon^{\prime}_{i} ,i = x,y,z\) :

First-order derivative of the lifting pipe displacements with respect to z

\(A_{{\text{i}}}\) :

Internal cross-sectional area of the lifting pipe

\(\dot{u}_{i} ,i = 1,2,3\) :

First-order derivative of lifting pipe displacements function with respect to time for coordinate system \(x,y,z\)

\(m_{\upsilon }\) :

Mass of lifting pipe unit length

\(m_{i}\) :

Mass of the multiphase flow velocity in the lifting pipe unit

\(F_{{\text{D}}} \left( {z,t} \right)\) :

Drag force in the IL direction

\(f_{x} \left( {z,t} \right)\) :

High-speed fluid impact loads in the lifting pipe in the x-direction

\(f_{z} \left( {z,t} \right)\) :

High-speed fluid impact loads in the lifting pipe in the z-directions

\(W_{{\text{f}}}\) :

Fluid viscous damping

\(\alpha_{2} \left( t \right)\) :

Deflection angles of the lower micro-segments in the x-directions

\(\varphi_{2} \left( t \right)\) :

Deflection angles of the lower micro-segments in the y-directions

\(\rho_{w}\) :

Density of seawater

\(D_{{\text{i}}}\) :

Inner diameter of the lifting pipe

\(m_{{\text{a}}}\) :

Additional mass per unit length of pipe string

\(u_{{{\text{boat}}}} (t)\) :

Platform heave displacement

\(U_{c}\) :

External flow velocity of lifting pipe

\(C^{\prime}_{{\text{d}}}\), \(C^{\prime}_{{\text{l}}}\) :

Reference drag force coefficient and reference lift force coefficient

\(\omega_{{\text{s}}}\) :

Shedding frequency of wake vortex

\(\varepsilon_{x} ,\varepsilon_{y} ,A_{x} ,A_{y}\) :

Dimensionless parameters

\(\rho_{{\text{s}}}\) :

Density of solid particles

\(\Delta V\) :

Selected control volume

\(\alpha\) :

Inclination angle of pipe string

\(\tau_{m}\) :

Wall shear stress

\(m_{{\text{p}}}\) :

Mass of the platform

\(A_{w}\) :

Area of the platform at sea level

\(\overline{F}_{z}\) :

Random heave wave exciting force on the platform

\(\overline{\varepsilon }_{i}\) :

Initial phase of the \(i\)-th harmonic component

\(a_{i}\) :

Amplitude of the \(i\)-th harmonic component

\(S\left( \omega \right)\) :

Random wave spectrum

\(\omega\) :

The circular frequency

\(T_{1/3}\) :

Significant period

\(T_{{\text{p}}}\) :

Peak period

\(\sigma\) :

Peak shape coefficient

\(k\) :

Wave number

\(z_{{{\text{plate}}}}\) :

Depth of heave plate

\(D\) :

Fatigue cumulative damage

\(r\) :

Damage coefficient

\(D_{{\text{c}}}\) :

Critical fatigue damage

\(r_{\max }\) :

Component forces of the transverse damage coefficient

\(N_{\max }\) :

Number of cycles under the action of maximum stress

\(r_{i}\) :

Damage coefficient

\(n_{i}\) :

Number of cycles

\(a_{i}\) :

Percentage for the number

\(\sigma_{\max }\) :

Maximum stress in multistage stress

\(N_{{{\text{f}}i}}\) :

Fatigue life under action of the single \(\sigma_{i}\) stress

\(p^{\prime}\), \(q\) :

Material constants

\(A_{0}\) :

Strength degradation coefficient

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Funding

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 52105125 and 11972145), Fellowship of China Postdoctoral Science Foundation (Grant Nos. 2021TQ0273 and 2022M712643), Natural Science Foundation Project of Sichuan Province (Grant No. 2022NSFSC1922), Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences (No. E229kf15) and Innovative Research Groups of Natural Science Foundation of Hebei Province (A2020202002).

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Authors and Affiliations

  1. School of Mechanical Engineering, Hebei University of Technology, Tianjin, 300401, China

    Xiaoqiang Guo, Xinghan Chen, Libin Zhao & Xinye Li

  2. Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou, 510640, China

    Xiaoqiang Guo

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Guo, X., Chen, X., Zhao, L. et al. Multi-field coupling multiple nonlinear vibration model and fatigue failure mechanism of deep-ocean mining hydraulic lifting pipe. Nonlinear Dyn 111, 16777–16811 (2023). https://doi.org/10.1007/s11071-023-08733-y

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