## Calculation of Towing Resistance of Jack-up Offshore Platform

AN Tao,, LIN Zengyong, BAI Jian

Shengli Petroleum Engineering Company, Sinopec, Dongying 257000, Shandong, China

Received: 2022-07-7   Revised: 2022-07-25   Accepted: 2022-08-22

Abstract

In the course of towing of offshore platform, it is of great significance to calculate the towing resistance ahead of time and select the main tugboat with proper power for towing safety. In this paper, the calculation formulas or recommended methods for towing resistance of mainstream classification societies were investigated, and a CFD/AQWA finite element numerical simulation was conducted for the typical jack-up offshore platform in Shengli Petroleum Engineering Company.Based on the comparative analysis of the results, a suitable model for the calculation of towing resistance of platforms in domestic waters was optimized, and a suitable towing factor of safety was proposed.

Keywords： towing resistance; calculation model; finite element; offshore platform

AN Tao, LIN Zengyong, BAI Jian. Calculation of Towing Resistance of Jack-up Offshore Platform[J]. Journal of Shanghai Jiaotong University, 2023, 57(S1): 108-113 doi:10.16183/j.cnki.jsjtu.2023.S1.03

## 1 国内外规范算法介绍

Tab.1  Environment conditions for calculation of towing resistance in different specifications

### 1.1 国内规范算法

$Rf=1.67A1V1.83×10-3 Rb=0.147δA2V1.74+0.15VR2=0.5ρV2ΣCsAi10-3$

### 1.2 各主流船级社拖航阻力公式

DNV船级社没有直接针对拖航过程的阻力公式,但规范中有关于拖航中平台受到的风阻力公式和波流力计算的简单公式以及水动力学推荐算法,水动力学计算需要用专门的水动力学软件进行计算.

(1) 辐射问题.在没有入射波的情况下,结构被迫以刚体运动模式与波频率振荡,所产生的载荷通常用附加质量、阻尼和恢复载荷来表示:

$Fk(r)=-Akjd2ξjdt2-Bkjdξjdt-Ckjξj$

(2) 衍射问题.其中结构受到运动限制,并受到入射波的激发,由此产生的荷载为波浪激励荷载,即

$Fk(d)=fk(ω)e-iωt$

### 1.3 不同计算模型验证分析

Tab.2  Results of towing resistance obtained by algorithm of Guidance for China Classification Society

11310691069
24510891089
39911221122
418311731173
530612471247
648213551355

Tab.3  Results of towing resistance obtained by algorithm of CCS taking into account wave resistance

kn

11076.91086.21101.81123.61151.7
21112.31131.01162.21205.91262.0
31169.91197.91244.71310.21394.4
41256.31293.71356.11443.41555.6
51382.01428.81506.71615.91756.2
61562.11618.31711.81842.82011.2

Tab.4  Results of towing resistance obtained by using specification algorithm of Korean Register of Shipping

11405
21609
31908
42302
52791
63375

## 2 水动力学典型工况校核计算

### 图1

Fig.1   Schematic diagram of a large jack-up platform

Tab.5  Data of a large jack-up platform

### 2.1 CFD数值计算模型

(1) 平台模型按照缩尺比1∶1绘制,忽略物理模型主甲板以上组件,忽略平台艏部、尾部存在的三桩腿开口,如图2所示.

### 图2

Fig.2   Numerical computation model-platform model

(2) 计算域长330 m、宽300 m、高50 m,如图3所示.

### 图3

Fig.3   Numerical computation model-computational domain

(3) 网格选用切割体网格单元,平台湿表面选用面加密,平台周围流场采用双层加密,并针对水体自由表面(根据不同波浪,加密范围略有不同)和浅水水底进行单独加密,网格总数约为316×104/485×104,如图4所示.

### 图4

Fig.4   CFD numerical model-grid

(4) 湍流模型为k-ε RANS模型.

(5) 时间步长为10 ms,内部迭代数为5.

Tab.6  Statistics of total resistance of platform in static water and waves calculated by CFD

m

s
X方向

kN
X方向

kN

kN
11 kn静水--11.3211.8011.56
22 kn静水--59.357.958.6
33 kn静水--138.9125.1132.5

### 图5

Fig.5   Numerical model of potential flow (platform model)

### 图6

Fig.6   Numerical model of potential flow (fluid domain)

### 图7

Fig.7   Numerical model of potential flow (grid)

(1) 平台模型按照缩尺比1∶1绘制,忽略物理模型主甲板以上组件,忽略平台艏部、尾部存在的三桩腿开口.

(2) 流体域长400 m、宽400 m、水深15 m.

(3) 网格最大尺寸为1 m,允许的误差大小为0.5 m,最大计算频率为0.545 Hz,网格总数为 24945.

(4) 不规则波浪采用P-M波谱.

(5) 时间步长为0.1 s.

Tab.7  Statistics of drift force calculated by potential flow

11634.51
228106.87
338180.52
448240.66
558320.00

Tab.8  Hydrodynamic towing resistance at 1 kn

kN

kN

11061.311.561.3134.511108.68
21061.311.567.09106.871186.82
31061.311.5628.55320.001421.41

## 3 拖航阻力计算模型选择

Tab.9  Comparison of towing resistance at a towing speed of 1 kn, a wave height of 5 m, and a wind of 20.6 m/s

CCS拖航指南1069
CCS考虑波浪算法1152

## 4 拖航安全系数优选

Tab.10  Statistics of towing force of towing pillar of a typical platform

(风速20 m/s;

0.5 m/s)/kN

(1.05)

(1.1)

(1.25)
1作业X号36.238.0139.845.3
2作业X号37.138.9640.846.4
3作业X号41.543.5845.751.9
4胜利X号60.263.2166.275.3
5胜利X号86.891.1495.5108.5

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