ANALYSIS OF VORTEX-INDUCED VIBRATION FOR A CANTILEVER RISER IN A DEEP-SEA MINING SYSTEM
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摘要: 不同于传统的海洋立管, 深海采矿系统中的垂直提升管道可以被视为一个底部无约束的柔性悬臂式立管, 工作过程中同样面临涡激振动和柔性变形问题. 本文采用一种无网格离散涡方法和有限元耦合的准三维时域求解数值模型, 系统性地研究了不同流速下悬臂式立管的涡激振动问题. 结果表明: 悬臂式立管的横向振动模态阶数随折合速度增加而增大, 在一定折合速度范围内主导振动模态保持不变; 当主导模态转变时, 对应的横向振幅会发生突降, 但是当新的高阶模态被激发后, 立管振幅随来流速度增加而再次逐渐增大; 在相同的振动模态下, 立管底部位移均方根值随折合速度线性增加, 主导振动频率在模态转变时会出现跳跃现象; 特别地, 本文讨论了三阶主导模态下悬臂式立管的振动响应, 无约束的立管底部呈现出较大的振动能量, 且振幅的驻波特征随折合速度增加而逐渐增强; 本文比较了两端铰支立管与悬臂式立管的涡激振动响应特征, 两者在振幅和主导振动频率两方面均表现出了相同的变化趋势.Abstract: Different from the traditional marine riser, the vertical lifting pipeline in the deep-sea mining system can be regarded as a flexible cantilever riser with an unconstrained bottom end. Likewise, problems in terms of vortex-induced vibrations (VIVs) and flexible deformations can be encountered during operation. In this paper, a quasi-three-dimensional time-domain numerical model coupled with the discrete vortex method (DVM) and finite element method (FEM) is employed in the time domain. Systematic simulations have been carried out to investigate the VIVs of a cantilever riser under different current speeds. The results indicate that, for a cantilever riser, the transverse vibration mode number rises with increasing the reduced velocity. In a certain range of reduced velocities, the dominant vibration modes remain unchanged. When the modal transition occurs, the corresponding vibration amplitudes can abruptly drop. However, when the new high-order mode is excited, vibration amplitudes of the riser again gradually increase with increasing the incoming velocities. In the same vibration mode, the root-mean-squared values for the bottom displacements of the riser linearly rise with the reduced velocities. When vibration mode changes, a jump phenomenon for the dominant vibration frequencies can be observed. Especially, the present work discusses the vibration responses of the cantilever riser in the three-order dominant mode. It can be found that the unconstrained bottom end of the riser exhibits relatively large vibration energy. The standing wave characteristics of the vibration amplitudes gradually enhance with the increase of the reduced velocities. The VIV response characteristics of a two-ends hinged riser and a cantilever riser are compared in this investigation, both of which exhibit the same variation tendency in terms of amplitude and dominant vibration frequency.
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图 3 不同单元数立管的横向位移均方根值
Figure 3. RMS amplitudes of the transverse displacements for the riser models with various element numbers
图 4 不同流速下的柔性立管横向振动响应((a), (c)振动位移包络线; (b), (d)位移均方根值)
Figure 4. Vibration response envelopes of a flexible riser under different current speeds ((a), (c) vibration amplitude envelopes; (b), (d) RMS displacements)
图 5 悬臂式立管前8阶固有频率和振型
Figure 5. First eight-order natural frequencies and modal shapes for a cantilever riser
图 6 不同折合速度下的横向振幅均方根值
Figure 6. RMS vibration amplitudes in the transverse direction under a wide range of reduced velocities
图 7 不同折合速度下的柔性立管横向振动响应 ((a)~(d)位移均方根值; (e)~(h)振动位移包络线)
Figure 7. Vibration response envelopes of a flexible riser under different reduced velocities ((a)~(d) RMS amplitudes; (e)~(h) vibration amplitude envelopes)
图 8 立管底部横向位移均方根值
Figure 8. RMS amplitude of the transverse displacement at the bottom for the riser
图 10 立管横向振动频率空间分布 ((a)~(g)
${U_r}$ = 24~36)Figure 10. Spatial distribution of transverse vibration frequency for the riser ((a)~(g)
${U_r}$ = 24~36)
11 立管泄涡频率空间分布 ((a)~(g)
${U_r}$ = 24~36)11. Spatial distribution of vortex shedding frequency for the riser ((a)~(g)
${U_r}$ = 24~36)
11 立管泄涡频率空间分布 ((a)~(g)
${U_r}$ = 24~36) (续)11. Spatial distribution of vortex shedding frequency for the riser ((a)~(g)
${U_r}$ = 24~36) (continued)
图 12 立管不同位置的振幅时空演化 ((a)~(g)
${U_r}$ = 24~36)Figure 12. Temporal-spatial evolution of transverse vibration amplitude along the riser span ((a)~(g)
${U_r}$ = 24~36)
图 13 瞬态涡量场 ((a)~(d)
${U_r}$ = 24~30)Figure 13. Instantaneous vorticity field ((a)~(d)
${U_r}$ = 24~36)
图 14 两端铰支立管前8阶固有频率和振型
Figure 14. First eight-order natural frequencies and modal shapes for a riser hinged at both ends
图 15 沿立管展向最大的横向位移均方根值
Figure 15. Maximum RMS amplitude of the transverse displacement along the riser span
图 16 立管横向振动的主导频率比
Figure 16. Dominant frequency ratio of the transverse vibration for the riser
图 17 立管不同位置的振幅时空演化 ((a)~(c)
${U_r}$ = 16~20)Figure 17. Temporal-spatial evolution of transverse vibration amplitude along the riser span ((a)~(c)
${U_r}$ = 16~20)Parameters Values Units length $L$ 9.63 m external diameter $D$ 0.02 m internal diameter $d$ 0.0191 m mass per unit length $m$ 0.7 kg mass ratio ${m^*}$ 2.23 − aspect ratio $L/D$ 481.5 − Young modulus $ E $ 102.5 GPa top tension ${T_{{\rm{top}}} }$ 817 N structural damping ratio $\xi $ 0.003 − current speed ${u_\infty }$ 0.42, 0.84 m/s Reynolds number $Re$ 8400, 16800 − fluid density $ \rho $ 1000 kg/m3 kinematic viscosity $\nu $ 1 × 10−6 m2/s 
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