﻿ 锚链预张力对 FDPSO 运动响应的影响
 舰船科学技术  2017, Vol. 39 Issue (3): 23-28 PDF

The effect of mooring line pre-tension on FDPSO's motion
YAN Liu, REN Hui-long, SUN Yan-long, LIU Zhen-dong
Harbin Engineering University, College of Marine Engineering, Harbin 150001, China
Abstract: As a multifunction floating platform, Floating Drilling, Production, Storage and Offloading (FDPSO) combining the well-known Floating Production, Storage and Offloading (FPSO) with a drilling unit. For the environment condition of deep-water oilfield is very severe, the motion response and mooring line tension of FDPSO is a worthy topic of studying. In this study, the numerical time-domain coupled prediction method for the mooring line tension and motion response of FDPSO system is constructed by Ansys AQWA software. Furthermore, the results of a model test conducted in Harbin Engineering University are used to investigate the feasibility and validity of the commercial simulation. The effect of mooring line pre-tension on the response of FDPSO is studied by varying the pre-tension of mooring line during the calculation. The time series curve of the mooring line tension and motion response, and the comparison of motion spectrum and mooring line tension spectrum are provided in this article. The findings from this study have shown the pre-tension of mooring line has considerable influence on the surge, sway and roll motion's spectrum density distribution.
Key words: FDPSO     motion response     mooring line pre-tension
0 引　言

FDPSO 长期工作于深水海域，通过锚链系统来提供船体运动响应的恢复力。但FDPSO 受风浪影响比较大，对浪向角也比较敏感，抵抗恶劣海况的能力差。为了提高钻井船的工作效率，对其进行深入的水动力性能研究十分必要。

1 理论基础 1.1 绕射/辐射力

 ${\varPhi} (x,y,z,t) = \varphi (x,y,z){e^{ - i\omega t}} \text{，}$ (1)

 $\phi (x,y,z){e^{ - i\omega t}} = \left[ {\left( {{\phi _I} + {\phi _d}} \right) + \sum\limits_{j = 1}^6 {{\varphi _j}{x_j}} } \right]{e^{ - i\omega t}} \text{，}$ (2)

 ${\phi _I} = \frac{{ - ig\cosh [k(d + z)]{e^{ik(x\cos \theta + y\sin \theta )}}}}{{\omega \cosh (kd)}} \text{，}$ (3)

 $p = - \rho \frac{{\partial \Phi }}{{\partial t}} \text{，}$ (4)

 ${{F}} = - i\rho \omega {e^{ - i\omega }}\iint_{{S_B}} {\left( {{\phi _I} + {\phi _D}} \right){{n}}{\rm d}S} \text{，}$ (5)

 ${F_{ji}} = - \rho {\omega ^2}\iint\nolimits_{{S_B}} {{\phi _i}{n_j}{\rm d}S} , i,j = 1,2...6 \text{，}$ (6)

 ${F_{ji}} = {\rm{ - }}{A_{ji}}{\ddot x_i} - {B_{ji}}{\dot x_i} \text{，}$ (7)

 $F\left( \omega \right) = {F_j} + {F_{ji}} \text{，}$ (8)
 ${M_s}\left( \omega \right)\ddot x + {M_a}\left( \omega \right)\dot x + { C}\left( \omega \right)\dot x + {K_s}\left( \omega \right)x = F\left( \omega \right) \text{。}$ (9)

1.2 二阶平均漂移力

 $\begin{split}\\[-12pt]{{F}}_{strc}^{(2)} = & - \oint_{WL} {\frac{1}{2}} \rho g\zeta _r^2{{n}}{\rm d}l + {\iint_{{S_0}} {\frac{1}{2}\rho \left| {\nabla \phi } \right|} ^2}{{n}}{\rm d}S +\\& \iint_{{S_0}} {\rho (X \cdot \nabla \frac{{\partial \Phi }}{{\partial t}})} {{n}}{\rm d}S + {M_s}{{R}} \cdot {{\ddot X}_g} \text{，}\end{split}$ (10)
 $\begin{split}\\[-12pt]{{M}}_{strc}^{(2)}\! \!=\! & - \oint_{WL} \!\!{\frac{1}{2}} \rho g\zeta _r^2({{r}} \!\times\! {{n}}){\rm d}l \!+\!\!\! {\iint_{{S_0}} \!\!{\frac{1}{2}\rho \left| {\nabla \phi } \right|} ^2}\!\!({{r}} \!\times\! {{n}}){\rm d}S \!+\\& \iint_{{S_0}} {\rho (X \cdot \nabla \frac{{\partial \Phi }}{{\partial t}})} ({{r}} \times {{n}}){\rm d}S + {{{I}}_s}{{R}} \cdot {{\ddot X}_g} \text{。}\end{split}$ (11)

 $\begin{split}\\[-12pt]{{F}}_{}^{(2)}(t) \!=\! \!& \sum\limits_{i = 1}^N {\sum\limits_{j = 1}^N \!\!{\left. {\left\{ \!\!\!\!\!{\begin{array}{*{20}{c}}{P_{ij}^ - \cos [ - ({\omega _i} - {\omega _j})t + ({\varepsilon _i} - {\varepsilon _j})]}\\{ + P_{ij}^ + \cos [ - ({\omega _i} + {\omega _j})t + ({\varepsilon _i} + {\varepsilon _j})]}\end{array}} \right.} \!\!\!\!\!\right\}} }+ \\& \sum\limits_{i = 1}^N {\sum\limits_{j = 1}^N {\left. {\left\{ \!\!\!\!\!{\begin{array}{*{20}{c}}{Q_{ij}^ - \sin [ - ({\omega _i} - {\omega _j})t + ({\varepsilon _i} - {\varepsilon _j})]}\\{ + Q_{ij}^ + \sin [ - ({\omega _i} + {\omega _j})t + ({\varepsilon _i} + {\varepsilon _j})]}\end{array}} \!\!\!\!\!\right.} \right\}} } \text{，}\end{split}$ (12)

 $\begin{split}P_{ij}^ \pm = & - \oint_{WL} {\frac{1}{4}} \rho g{\zeta _i}{\zeta _j}\cos ({\varepsilon _i} - {\varepsilon _j}){{n}}{\rm d}l +\\& \iint_{{S_0}} {\frac{1}{4}\rho \left| {\nabla {\phi _i}} \right|} \left| {\nabla {\phi _j}} \right|{{n}}{\rm d}S+ \\& \iint_{{S_0}} {\frac{1}{2}\rho ({X_i} \cdot \nabla \frac{{\partial {\Phi _j}}}{{\partial t}})} {{n}}{\rm d}S+ \\& \frac{1}{2}{M_s}{{{R}}_i} \cdot {{\ddot X}_{gj}} + \iint_{{S_0}} {\rho \frac{{\partial {\Phi ^2}}}{{\partial t}}} {{n}}{\rm d}S \text{。}\end{split}$ (13)
1.3 FDPSO 的时域耦合分析
 $\begin{split}\\[-12pt]& [{M_s} + {M_a}\left( t \right)]\ddot x(t) + C\dot x(t) + {K_s}x(t) = \\& {F_{wave}}(t) + {F_{moor}}(t) + {F_{current}}(t) + {F_{wind}}(t) \text{。}\end{split}$ (14)

2 模型试验 2.1 FDPSO 设计参数

 图 1 FDPSO 模型 Fig. 1 The model of FDPSO

 图 2 锚泊系统布置 Fig. 2 Arrangement of mooring system

2.2 环境参数

 $\begin{array}{l}S(\omega ) = 487[1 - 0.287\ln (\gamma )]\frac{{H_s^2}}{{T_p^4}}{\omega ^{ - 5}}\\ \cdot \exp \left( {\frac{{ - 1948}}{{T_p^4}}{\omega ^{ - 4}}} \right){\gamma ^{\exp \left[ {\frac{{ - {{(0.159\omega {T_p} - 1)}^2}}}{{2{\sigma ^2}}}} \right]} \text{。}} \end{array}$ (15)

3 结果与讨论

 图 3 FDPSO 主船体水动力网格效果图 Fig. 3 Hydrodynamic model of FDPSO
3.1 理论计算结果与试验结果对比分析

3.2 锚链线预张力对 FDPSO 运动响应的影响

 图 5 运动响应谱 Fig. 5 Spectrum of the motion

 图 6 FDPSO 的锚链力和合力（CaseⅢ） Fig. 6 Mooring force and total force of FDPSO （CaseⅢ）
4 结　语

1）低频运动是 FDPSO 系统纵荡和横荡运动的主要成分，随着锚链预张力的减小，纵荡和横荡运动响应的幅值会显著增大，在锚链系统的设计中应着重考虑。

2）对于垂荡、横摇和纵摇波频响应占主要部分，锚链预张力的变化对横摇运动的影响比较大而对垂荡和纵摇的影响比较小。随着预张力的增大，横摇运动响应谱的峰值周期逐渐变大。

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