# Analysis of Fluid–Structure Coupling Vibration Mechanism for Subsea Tree Pipeline Combined with Fluent and Ansys Workbench

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## Abstract

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## 1. Introduction

- AnsysFluent and AnsysCFX have been usually used to analyze fluid or fluid–structure coupling analysis in the past. In this paper, amethod based on the coupling between Fluent and Ansys Workbench structural mechanics module was adopted to conduct the analysis;
- In this paper, the research and analysis of pipeline vibration mechanism were applied to subsea tree to analyze the vibration mechanism of underwater subsea tree pipeline;
- This paper puts forward the measures to reduce the vibration of subsea tree pipelines and provides construction advice for the safe production of subsea trees.

## 2. Fluid–Structure Coupling Vibration Analysis Method of Subsea Tree Pipeline

- Friction coupling: due to the molecular interaction between the fluid and the pipe wall in contact with it, that is, the viscosity of the fluid, which not only leads to the friction between the fluid and the solid but also causes the internal friction of the fluid;
- Poisson coupling: related to the material properties of the pipe. It is caused by the periodic change of pressure caused by the change of a parameter of the flow field in the pipe and the local interaction between the pipe walls. It is named because it is related to Poisson’s ratio of the pipe;
- Connection coupling: refers to a strong local coupling effect at the pipeline connection. This coupling is caused by the instability of fluid pressure, which will cause potential safety hazards at the pipeline connection;
- Bourdon coupling: often acts on the bend section of the pipeline because the existence of the bend section of the pipeline forces the pressure change caused by changing the flow channel;simultaneously, the changed fluid pressure will also react on the bend section to make it straight.

- 5.
- Classical water hammer model [29]: because of the convenience and practicability of its mathematical theory, it is widely used in some industrial fields. In 2021, Zhang et.al. deduced the differential equation of lateral vibration of the fluid conveying pipeline. The exponential decay function is introduced to simulate the oscillating decay characteristics of the flow velocity when water hammer occurs, and the expression of the dynamic instability region of the fluid conveying pipeline under the action of the internally excited oscillating decay flow is derived;
- 6.
- Beam model [30]: Guo made a summary in the paper. The basic assumptions are: (1) the fluid is not dry and incompressible; (2) the tube is analyzed as a beam model; (3) the tube is only on a plane. The internal vibration does not consider the influence of shear deformation and the moment of inertia of the section. In addition, Yang Ke and Zhang Lixiang [31] used the beam theory to obtain the fluid–solid coupling axial vibration of a liquid-filled pipe. RenJianting et al. [32] established the waveguide equation of the pipeline fluid–solid composite system using the straight beam model.
- 7.
- Shell model [33]: Ni used the shell model to study the distribution of shear stress between layers of laminated structures. A test sample tube was made using this distribution law, and a short-term hydraulic blasting test was carried out. At the same time, the test verified that the effect of delamination defects on the burst pressure of the composite pipe is related to the interlaminar shear stress.

## 3. Analysis of Tree Flow Field Based On Computational Fluid Dynamics

#### 3.1. Introduction To Subsea Trees

- The device is installed in the tubing hanger inside the body of the Christmas tree;
- The Christmas tree valve group is installed on the side of the tubing hanger;
- During the installation process, the Christmas tree body, is installed first, followed by the tubing hanger and production tubing.

#### 3.2. Environmental Conditions of Subsea Tree Operation

#### 3.3. Modeling and Mesh Analysis of Subsea Tree Pipeline Fluid Domain

#### 3.4. Fluent calculation results and analysis

#### 3.5. Fluent Calculation Results and Analysis

## 4. Two-Way Fluid–Structure Coupling Analysis of Subsea Tree Pipeline

#### 4.1. Modal Calculation Analysis of Underwater Subsea Tree

#### 4.2. Thermal Analysis of the Subsea Tree

## 5. Experimental Device and Scheme Design

^{2}; the average y-axis acceleration was 0.71 mm/s

^{2}; the average z-axis acceleration was 0.135 mm/s

^{2}, as shown in Figure 20. The y-axis acceleration was the largest. The formula could be obtained, represents the distance the water flows through, represents the initial velocity of the water flow, represents the time, and represents the acceleration of the water flow, the maximum amplitude at the entrance pointwas 0.4 mm, and the smallest third-order mode maximum vibration amplitude was 0.48 mm; that was, the actuallymeasured amplitude did not exceed the maximum vibration amplitude calculated by the numerical simulation.

^{2}and the average x-axis acceleration at the exit was 0.46 mm/s

^{2}, both of which were smaller than the average x-axis acceleration at a right-angle corner. The average y-axis acceleration at the entrance was 0.69 mm/s

^{2}, and the average y-axis acceleration at the exit was 0.59 mm/s

^{2}, both of which were smaller than the average y-axis acceleration at a right-angle corner. The z-axis acceleration line graph at the exit and the entrance, the average z-axis acceleration at the entrance was 0.107 mm/s

^{2}, and the average z-axis acceleration at the exit was 0.099 mm/s

^{2}, both of which were smaller than the average z-axis acceleration at a right-angle corner. In summary, the vibration amplitude at the right-angle corner of the trigeminal pipeline was the largest, which verified the correctness of the conclusions that the fluid in Section 3 and Section 4.

## 6. Conclusions

- There willinevitably be a bend, diameter, branch, valve and other pipe components in the subsea tree pipeline. The existence of these exciting sources will produce exciting forces. Pipe layout should strive to be simple, as far as possible to reduce unnecessary elbow, size and other easy-to-produce vibration force pipe fittings. At the turning point of the piping system, elbows with a large curvature radius should be used as muchas possible instead of elbows; inclined connections should be used instead of right-angle connections, and forward connections should be used. These measures can effectively reduce the mechanical vibration amplitude, thereby reducing the harm caused by vibration;
- Support stiffness is an important factor affecting the natural frequency of the pipeline. The stronger the brace’s stiffness, the more influence the stiffness of the bracewill haveon the natural frequency of the system. The lower the support stiffness, the lower the natural frequency value of the pipe system, and vice versa; the stronger the support stiffness, the higher the natural frequency. Therefore, when designing the support, the stiffness of the support should be large, and the mass of the support should be small, and the connection between the pipe and the support should be as rigid as possible;
- The vibration is increasedwhen the pressure change frequency of the tree air inlet is close to the natural frequency of the pipeline. Attention should be paid to the frequency obtained from the modal analysis to avoid resonance and to strengthen the fixation at large displacement. Where the vibration amplitude is the largest under the first six modes frequency, these frequencies should be avoided in practical work, and measures should be taken to strengthen the fixing of the top.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Analysis of subsea tree meshing. (

**a**) Subsea treemeshing; (

**b**) local mesh amplification of the throttle valve and tubing hanger body.

**Figure 14.**Overall temperature distribution cloud diagram for the subsea tree (

**a**) under condition 1 and (

**b**) under condition 2.

**Figure 15.**Overall temperature distribution cloud diagram for the subsea tree (

**a**) under condition 1 and (

**b**) under condition 2.

**Figure 20.**Comparison of acceleration in each direction of entrance and exit. (

**a**) x-axis acceleration; (

**b**) y-axis acceleration; (

**c**) z-axis acceleration.

Flow Field Calculation Method | Flow Regime | Turbulence Model | Y-axis Acceleration (m/s^{2}) | Ambient Temperature (K) | Fluid Material | Solving Algorithm | Residual Accuracy | Number of Iterations (Times) |
---|---|---|---|---|---|---|---|---|

Implicit algorithm | Turbulence | k-Epsilon | −9.81 | 292.65 | CH_{4} | SIMPLE algorithm | 0.00001 | 500 |

Operating Condition | Maximum Pressure (MPa) | Minimum Pressure (MPa) | Maximum Speed (m/s) | Minimum Speed (m/s) |
---|---|---|---|---|

Condition 1 | 3.8467 | 3.7907 | 70.7225 | 1.08 |

Condition 2 | 12.1387 | 12.0931 | 21.5945 | 1.08 |

Mesh Style | Algorithm Processing Type | Turbulence Modeling Type | Outer Wall Pressure (MPa) | Ambient Temperature (K) | Fluid Material | Solver Type |
---|---|---|---|---|---|---|

Tetrahedral mesh | Mechanical | k-Epsilon | 4.9 | 292.65 | CH_{4} | Fluent |

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**MDPI and ACS Style**

Wu, G.; Zhao, X.; Shi, D.; Wu, X. Analysis of Fluid–Structure Coupling Vibration Mechanism for Subsea Tree Pipeline Combined with Fluent and Ansys Workbench. *Water* **2021**, *13*, 955.
https://doi.org/10.3390/w13070955

**AMA Style**

Wu G, Zhao X, Shi D, Wu X. Analysis of Fluid–Structure Coupling Vibration Mechanism for Subsea Tree Pipeline Combined with Fluent and Ansys Workbench. *Water*. 2021; 13(7):955.
https://doi.org/10.3390/w13070955

**Chicago/Turabian Style**

Wu, Gongxing, Xiaolong Zhao, Danda Shi, and Xiaodong Wu. 2021. "Analysis of Fluid–Structure Coupling Vibration Mechanism for Subsea Tree Pipeline Combined with Fluent and Ansys Workbench" *Water* 13, no. 7: 955.
https://doi.org/10.3390/w13070955