# Investigation of Dynamic Behavior of Ultra-Large Cold-Water Pipes for Ocean Thermal Energy Conversion

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## Abstract

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## 1. Introduction

## 2. Analytical Simulation

## 3. Results and Discussion

#### 3.1. Parameter Sensitivity Analysis

#### 3.1.1. Effects of Waves

#### 3.1.2. Effects of the Clump Weight

#### 3.1.3. Effects of Internal Flow Velocity

#### 3.1.4. Effects of Current Velocity

#### 3.2. Orthogonal Analysis of Key Parameters

#### 3.2.1. Analysis of Orthogonal Experiments

^{4}orthogonal test form was used to carry out the orthogonal test design, and the protocol was developed concerning the orthogonal form, as shown in Table 6.

#### 3.2.2. Simulation Data Analysis

#### 3.2.3. Extremum Difference Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**The lateral displacement and max bending moment of the pipe with respect to different wave intensities.

**Figure 7.**The transverse displacement and max bending moment of the pipe with respect to different clump weights at the bottom.

**Figure 8.**The transverse displacement and bending moment of the pipe with respect to the internal flow velocity.

**Figure 9.**The transverse displacement and max bending moment of the pipe with respect to the external flow velocity.

Nomenclature | Description |
---|---|

EI | Bending stiffness (N/m^{2}) |

L | Pipe length (m) |

M_{p} | Mass of the internal flow per unit length (kg/m) |

M_{f} | Mass of the pipe per unit length (kg/m) |

T | Axial equivalent tension (N) |

U | Velocity of the internal flow (m/s) |

$\varphi (x,t)$ | Transverse displacement of the pipe (m) |

A_{f} | Internal cross-sectional areas (m^{2}) |

A_{0} | External cross-sectional areas (m^{2}) |

${\rho}_{w}$ | Density of the seawater (kg/m^{3}) |

C_{a} | Added mass coefficient |

${P}_{i}$ | Internal pressure of the pipe |

${P}_{0}$ | External pressure of the pipe |

C_{d} | Adapted drag coefficient |

Property | Value |
---|---|

Bending stiffness (Gpa) | 30 |

Inner diameter (m) Outer diameter (m) | 1.5 1.6 |

Density of the seawater (kg/m^{3})The density of the pipe (kg/m ^{3}) | 1025 1760 |

Pipe length (m) | 1000 |

Axial equivalent tension | 0 |

External flow velocity (m/s) | 1.09 |

Velocity of the internal flow (m/s) | 5.0 |

Top fluid pressure (Pa) | $1.0\times {10}^{5}$ |

Poisson’s ratio | 0.3 |

Adapted drag coefficient Additional mass coefficient | 1.0 1.0 |

Pipe Section Location | Numerical Simulation Method (m) | DQM Method (m) |
---|---|---|

0.1 | 0.8536 | 0.8934 |

0.3 | 0.4952 | 0.4879 |

0.5 | 0.3016 | 0.2991 |

0.7 | 0.1954 | 0.2047 |

0.9 | 0.1187 | 0.1152 |

Periodicity (Year) | 1 | 10 | 100 | |
---|---|---|---|---|

Wave | Significant wave height (m) | 4.8 | 5.8 | 6.5 |

Max wave height (m) | 8.3 | 10.0 | 11.3 | |

Period (s) | 7.8 | 9.0 | 9.8 |

Horizontal | Factors | |||
---|---|---|---|---|

Wave (m) | Current (m/s) | Internal Flow Velocity (m/s) | The Clump Weight (t) | |

1 | 4.8 | 0.99 | 2 | 900 |

2 | 5.8 | 1.09 | 4 | 1000 |

3 | 6.5 | 1.42 | 6 | 1100 |

Number | Wave (m) | Current (m/s) | Internal Flow Velocity (m/s) | The Clump Weight (t) |
---|---|---|---|---|

1 | 4.8 | 0.99 | 2 | 900 |

2 | 4.8 | 1.09 | 4 | 1000 |

3 | 4.8 | 1.42 | 6 | 1100 |

4 | 5.8 | 0.99 | 4 | 1100 |

5 | 5.8 | 1.09 | 6 | 900 |

6 | 5.8 | 1.42 | 2 | 1000 |

7 | 6.5 | 0.99 | 6 | 1000 |

8 | 6.5 | 1.09 | 2 | 1100 |

9 | 6.5 | 1.42 | 4 | 900 |

Numbers | Max Lateral Displacement (m) | Max Bending Moment (kN.m) |
---|---|---|

1 | 41.46 | 1854.8 |

2 | 46.8 | 1806.88 |

3 | 72.33 | 1910.79 |

4 | 34.73 | 1668.64 |

5 | 51.57 | 1892.18 |

6 | 78.35 | 1950.59 |

7 | 37.96 | 1446.81 |

8 | 42.88 | 1417.94 |

9 | 86.16 | 1840.65 |

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**MDPI and ACS Style**

Zhang, Y.; Zheng, M.; Zhang, L.; Zhang, C.; Tan, J.; Zhang, Y.; Duan, M.
Investigation of Dynamic Behavior of Ultra-Large Cold-Water Pipes for Ocean Thermal Energy Conversion. *Dynamics* **2023**, *3*, 468-487.
https://doi.org/10.3390/dynamics3030025

**AMA Style**

Zhang Y, Zheng M, Zhang L, Zhang C, Tan J, Zhang Y, Duan M.
Investigation of Dynamic Behavior of Ultra-Large Cold-Water Pipes for Ocean Thermal Energy Conversion. *Dynamics*. 2023; 3(3):468-487.
https://doi.org/10.3390/dynamics3030025

**Chicago/Turabian Style**

Zhang, Yanfang, Miaozi Zheng, Li Zhang, Chaofei Zhang, Jian Tan, Yulong Zhang, and Menglan Duan.
2023. "Investigation of Dynamic Behavior of Ultra-Large Cold-Water Pipes for Ocean Thermal Energy Conversion" *Dynamics* 3, no. 3: 468-487.
https://doi.org/10.3390/dynamics3030025