﻿ 带通海减动结构的圆筒型FDPSO阻尼系数计算
 舰船科学技术  2023, Vol. 45 Issue (11): 113-118    DOI: 10.3404/j.issn.1672-7619.2023.11.022 PDF

1. 江苏科技大学 船舶与海洋工程学院，江苏 镇江 212003;
2. 上海外高桥造船海洋工程有限公司，上海 200131

Calculation of damping coefficient of cylindrical FDPSO with sea connected damping structure
ZHANG Bo1, LI Qing2, HUANG Meng-li1, CHEN Lin-feng1
1. School of Naval Architecture and Ocean Engineering, Jiangsu University of science and technology, Zhenjiang 212003, China;
2. Shanghai Waigaoqiao Shipbuilding and Offshore Engineering Co., Ltd, Shanghai 200131, China
Abstract: In the calculation of floating drilling production storage and unloading device with sea opening motion reduction structure When calculating the heave damping coefficient of (FDPSO), because the size of the sea hole is much smaller than the overall structure size, there will be some problems in the numerical analysis, such as complex meshing, increased amount of calculation, large errors in the calculation results, etc. in view of these problems, this paper puts forward the research idea of using FDPSO without sea hole instead of FDPSO with sea hole to calculate the heave damping coefficient, and through theoretical derivation and The calculation proves the feasibility of this idea. Firstly, the hydrodynamic calculation software Ansys-Aqwa based on three-dimensional potential flow theory is used to establish the structural models of FDPSO with sea hole and FDPSO without sea hole, the equivalent heave mass of FDPSO with and without sea holes is calculated (the sum of displacement and added mass). The calculation results show that the equivalent heave mass and natural period of FDPSO with and without sea holes of the same size are equal. According to the FDPSO motion theory, the sea hole has little influence on the analysis of the heave damping coefficient of FDPSO. The heave damping coefficient can be calculated by using the sea hole free FDPSO instead of the sea hole FDPSO. Then, the scale of 1:77.8 scale model of FDPSO without through sea hole is established, the heave free attenuation motion is calculated and analyzed by using the hydrodynamic calculation software STAR CCM+ based on three-dimensional viscous flow theory, and the heave damping coefficient is calculated according to the time history curve of free attenuation motion.
Key words: FDPSO     open sea structure     heave motion     equivalent heave mass     damping coefficient
0 引　言

1 分析理论 1.1 FDPSO运动理论

 ${{m}}\ddot y + c\dot y + ky = F。$ (1)

 $F = {F_{\text{v}}} + {F_a}，$ (2)
 ${F_{{a}}} = - {{\text{m}}_a}\ddot y 。$ (3)

 $(m + {m_a})\ddot y + c\dot y + ky = {F_{{v}}}，$ (4)

 $({m_1} + m_a^1)\ddot y + c\dot y + ky = F_v^1 ，$ (5)

 $({m_2} + m_a^2)\ddot y + c\dot y + ky = F_v^2。$ (6)

 $令 m + {m_a} = {m_\delta }。$ (7)

1.2 固有周期

FDPSO固有周期的表达式可表示为[8]

 ${T_j} = 2\text{π} \sqrt {\frac{{{M_j}}}{{{K_j}}}} 。$ (8)

2 FDPSO有无通海孔对比 2.1 分析模型

 图 1 FDPSO模型示意图 Fig. 1 Schematic diagram of FDPSO model

2.2 计算结果

 图 2 运动响应传递函数（RAOs） Fig. 2 Motion response transfer function (RAOs)

 图 3 垂荡附加质量 Fig. 3 Heave additional mass

 $F_v^1 \approx F_v^2 。$ (9)

3 FDPSO垂荡阻尼分析

3.1 分析模型

 图 4 FDPSO几何建模 Fig. 4 FDPSO geometric modeling
3.2 数值仿真计算 3.2.1 计算水域的建立

 图 5 计算域尺寸 Fig. 5 Calculation domain size
3.2.2 物理模型

 $\frac{{\partial \alpha }}{{\partial t}} + \nabla \cdot ({\boldsymbol{U}}\alpha ) + \nabla \cdot ({{\boldsymbol{U}}_r}(1 - \alpha )\alpha ) = 0。$

 $\left\{ \begin{gathered} \alpha = 0，{\text{ air}}，\\ 0 < \alpha < 1，{\text{ interface}}，\\ \alpha = 1，{\text{ water}} 。\\ \end{gathered} \right.$
3.2.3 网格划分

 图 6 网格划分 Fig. 6 Meshing
3.3 数值仿真结果及阻尼分析

3.3.1 数值计算结果

FDPSO上升过程和下降过程中速度最大时的局部流场如图7所示。

 图 7 FDPSO上升和下降过程速度最大时局部流场图 Fig. 7 Local flow field diagram of FDPSO at maximum speed during rising and falling process

FDPSO垂荡自由衰减运动位移和受力如图8所示。

 图 8 FDPSO垂荡衰减运动位移图和受力图 Fig. 8 FDPSO heave attenuation motion displacement diagram and stress diagram
3.3.2 阻尼系数计算理论

 图 9 阻尼比计算理论 Fig. 9 Damping ratio calculation theory
 $\frac{{{y_i}}}{{{y_{i + 1}}}} = \frac{{A{e^{ - \zeta \lambda {t_i}}}\cos ({\lambda _d} + \beta )}}{{A{e^{ - \zeta \lambda ({t_i} + {T_d})}}\cos \left[ {{\lambda _d}({t_i} + {t_d}) + \beta } \right]}}。$

 ${\lambda _d}{T_d} = 2{\text{π}}$

 $\frac{{{y_i}}}{{{y_{i + 1}}}} = {e^{\zeta \lambda {T_d}}}。$

 $\delta = \ln \frac{{{y_i}}}{{{y_{i + 1}}}} = \zeta \lambda {T_d} = \zeta \lambda \frac{{2{\text{π}} }}{{{\lambda _d}}} \approx \zeta 2{\text{π}} 。$ (10)

 $\zeta \approx \frac{1}{{2{\text{π}} }}\delta。$ (11)

 $\frac{{{y_i}}}{{{y_{i + N}}}} = {e^{\zeta \lambda N{T_d}}}，$

 $\ln \frac{{{y_i}}}{{{y_{i + N}}}} = \zeta \lambda N{T_d} = \zeta N\lambda \frac{{2{\text{π}} }}{{{\lambda _d}}} \approx \zeta N2{\text{π}} = N\delta ，$

 $\delta = \frac{1}{N}\ln \frac{{{y_i}}}{{{y_{i + N}}}}。$ (12)

3.3.3 阻尼系数和周期计算

 $\zeta = \frac{{{\zeta _1} + {\zeta _2} + {\zeta _3}}}{3} = 0.082\;5。$

 $T = 2.22\;{\rm{s}} 。$

4 结　语

1）南海海况谱峰周期通常在12～18 s之间[6]，传统FDPSO的垂荡固有周期很难避开南海海况谱峰周期，通过计算，本文研究的圆筒型FDPSO垂荡固有周期为19 s，远离南海波浪能量集中范围，相较于传统FDPSO其运动性能得到较大改善。

2）通过理论公式推导和数值计算，得到有通海孔FDPSO和无通海孔FDPSO的垂荡等效质量相等，验证了通海孔对求解FDPSO阻尼系数几乎没有影响。

3）在尺寸一致的情况下，本文求解的阻尼系数与文献[5]水池实验得出的阻尼系数仅相差5.17%，垂荡固有周期仅相差3.06%，从实验角度也验证了本文思路和方法的正确性，为在求解阻尼时存在类似问题提供了一种分析思路。

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