﻿ 基于泰勒展开边界元方法的某半潜式平台水动力计算分析
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (9): 1431-1437  DOI: 10.11990/jheu.201706055 0

### 引用本文

CHEN Jikang, WANG Hui, MA Shan, et al. Hydrodynamic calculation and analysis on a semi-submersible platform based on Taylor expansion boundary element method[J]. Journal of Harbin Engineering University, 2018, 39(9), 1431-1437. DOI: 10.11990/jheu.201706055.

### 文章历史

1. 哈尔滨工程大学 船舶工程学院, 黑龙江 哈尔滨 150001;
2. 上海交通大学 船舶海洋与建筑工程学院, 上海 200240

Hydrodynamic calculation and analysis on a semi-submersible platform based on Taylor expansion boundary element method
CHEN Jikang1, WANG Hui1,2, MA Shan1, DUAN Wenyang1, WANG Lijia1
1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China;
2. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China
Abstract: In order to study the prediction accuracy of the first-order Taylor expansion boundary element method for the hydrodynamic performance and the motion response of a semi-submersible platform, the calculation results were compared with those of the commercial software AQWA. On the basis of the experimental results, through the comparative analysis of the results of the two methods, it shows that the results of the first-order Taylor expansion boundary element method are in good agreement with AQWA, in addition, the method has a good convergence speed. The method can be used for the hydrodynamic analysis of a semi-submersible platform and the work in the paper can also provide a reference for the hydrodynamic response analysis of such platform.
Keywords: Taylor expansion boundary element method    AQWA    semi-submersible platform    hydrodynamic coefficient    wave force    motion response    mean drift force

1 浮式平台水动力分析

 $\mathit{\Phi } = {\mathit{\Phi }_0} + {\mathit{\Phi }_p} = {\mathop{\rm Re}\nolimits} \left( {\left( {{\varphi _0} + {\varphi _p}} \right){{\rm{e}}^{ - {\rm{i}}\omega t}}} \right)$ (1)

 ${\mathit{\Phi }_p} = \sum\limits_{j = 1}^6 {{v_j}{\varphi _j}} + {\varphi _7}$ (2)

 $\left\{ \begin{array}{l} {\nabla ^2}{\varphi _j} = 0,\;\;\;\;流场内,j = 1,2, \cdots ,7\\ \frac{{\partial {\varphi _j}}}{{\partial z}} - \frac{{{\omega ^2}}}{g}{\varphi _j} = 0,\;\;\;\;z = 0,j = 1,2, \cdots ,7\\ \frac{{\partial {\varphi _j}}}{{\partial n}} = {n_j},\;\;\;\;{S_H}\;上,j = 1,2, \cdots ,6\\ \frac{{\partial {\varphi _7}}}{{\partial \mathit{\boldsymbol{n}}}} = - \frac{{\partial {\varphi _0}}}{{\partial \mathit{\boldsymbol{n}}}},\;\;\;\;{S_H}\;上\\ \mathop {\lim }\limits_{R \to \infty } \sqrt R \left( {\frac{{\partial {\varphi _j}}}{{\partial R}} - {\rm{i}}{k_0}{\varphi _j}} \right) = 0,j = 1,2, \cdots ,7 \end{array} \right.$ (3)

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

 $\left( {\mathit{\boldsymbol{M}} + \mathit{\boldsymbol{\mu }}} \right)\mathit{\boldsymbol{\ddot \eta }} + \mathit{\boldsymbol{\lambda \dot \eta }} + \mathit{\boldsymbol{C\eta }} = \mathit{\boldsymbol{f}}$ (5)

 $\begin{gathered} {\mathit{\boldsymbol{F}}^{\left( 2 \right)}} = - \frac{{\rho g}}{4}\int\limits_{wl} {\left( {{\zeta _3} - {\chi _3}} \right){{\left( {{\zeta _3} - {\chi _3}} \right)}^ * }\frac{{\mathit{\boldsymbol{n}}{\text{d}}l}}{{\sqrt {1 - n_3^2} }}} - \hfill \\ \;\;\;\;\;\;\;\;\;\frac{\rho }{4}\iint\limits_{{S_H}} {\left( {\nabla \varphi \cdot \nabla {\varphi ^ * }} \right)\mathit{\boldsymbol{n}}{\text{d}}s} - \frac{{{\text{i}}\omega \rho }}{2}\iint\limits_{{S_H}} {\left( {{\mathit{\boldsymbol{\chi }}^ * } \cdot \nabla \varphi } \right)\mathit{\boldsymbol{n}}{\text{d}}s} + \hfill \\ \;\;\;\;\;\;\;\;\;\frac{1}{2}\mathit{\boldsymbol{\eta }}_R^ * \times \left[ {{\mathit{\boldsymbol{F}}^{\left( 1 \right)}} - \rho g{A_{wp}}\left( {{\eta _3} - {\eta _5}{x_f}} \right)\mathit{\boldsymbol{k}}} \right] \hfill \\ \end{gathered}$ (6)

2 一阶泰勒展开边界元方法

 $4{{\rm{\pi }} }\varphi \left( p \right) + \sum\limits_{j = 1}^N {\iint\limits_{\Delta {S_j}} {\varphi \left( q \right)\frac{{\partial G}}{{\partial {n_q}}}{\text{d}}s}} = \sum\limits_{j = 1}^N {\iint\limits_{\Delta {S_j}} {G\frac{{\partial \varphi \left( q \right)}}{{\partial n}}{\text{d}}s}}$ (7)

 $\varphi \left( q \right) = \varphi \left( {{q_0}} \right) + \bar \xi \frac{{\partial \varphi }}{{\partial \bar \xi }}\left| {_{{q_0}}} \right. + \bar \eta \frac{{\partial \varphi }}{{\partial \bar \eta }}\left| {_{{q_0}}} \right.$ (8)

 $2{{\rm{\pi }} }\frac{{\partial \varphi \left( p \right)}}{{\partial \bar x}} + \frac{\partial }{{\partial \bar x}}\iint\limits_{{S_H}} {\varphi \frac{{\partial G}}{{\partial {n_q}}}{\text{d}}{s_q}} = \frac{\partial }{{\partial \bar x}}\iint\limits_{{S_H}} {\frac{{\partial \varphi }}{{\partial n}}G{\text{d}}{s_q}}$ (9)
 $2{\rm{\pi }}\frac{{\partial \varphi \left( p \right)}}{{\partial \bar y}} + \frac{\partial }{{\partial \bar y}}\iint\limits_{{S_H}} {\varphi \frac{{\partial G}}{{\partial {n_q}}}{\text{d}}{s_q}} = \frac{\partial }{{\partial \bar y}}\iint\limits_{{S_H}} {\frac{{\partial \varphi }}{{\partial n}}G{\text{d}}{s_q}}$ (10)

 $\sum\limits_{m = 1}^3 {\sum\limits_{j = 1}^N {\left[ {{{\left( {\mathit{\boldsymbol{A}}_m^{ij}} \right)}_k}\left( {\mathit{\boldsymbol{u}}_m^j} \right)} \right]} } = \sum\limits_{j = 1}^N {\left( {\mathit{\boldsymbol{B}}_k^{ij}} \right){{\left( {\frac{{\partial \varphi }}{{\partial n}}} \right)}^j}}$ (11)

3 计算模型的建立

4 平台计算的结果与比较 4.1 一阶水动力系数比较分析

4.2 一阶波浪力比较分析

 Download: 图 4 一阶波浪力的比较 Fig. 4 The comparison of first-order wave force

4.3 一阶运动响应幅值比较分析

4.4 二阶平均波浪漂移力比较分析

 Download: 图 6 平均漂移力的比较 Fig. 6 The comparison of mean drift force

5 结论

1) 一阶泰勒展开边界元方法在半潜平台的运动响应的预报上，与试验结果吻合较好，有着较高的精度，可用于半潜式平台的运动响应的预报。

2) 一阶泰勒展开边界元方法计算的结果与基于常值分布源方法计算的数值结果吻合较好，尤其在平台的水动力系数与运动响应的计算上。通过对三种不同网格情况下的结果进行比较分析，说明一阶泰勒展开边界元方法具有良好的收敛性。

3) 针对求解具有尖角结构的浮体平均漂移力，本文采用的泰勒展开边界元法利用压力积分近场公式也可给出同远场公式精度一致的收敛性结果，特别适用于考虑多浮体干扰情况下单个浮体上波漂力计算，这是本文方法的一个特色和优势。

4) 当前采用一阶泰勒展开边界元方法对于平台垂荡运动共振频率附近的预报结果与试验结果存在较大的偏差，主要是由于当前采用的一阶泰勒展开边界元方法没有考虑垂荡方向的粘性阻尼修正造成的。

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