# Wheeled Capsule Threshold of Motion at Different Locations in a Horizontal Bend Pipeline Based on Hydraulic Capsule Pipeline Transportation

^{*}

## Abstract

**:**

## 1. Introduction

_{D}∝ V

^{2}, the higher velocity would provide a larger drag force to make the capsule more easily start moving. To testify to the opinion mentioned above, this research is divided into the following sections. The second section presents the physical experiment’s arrangement. The third section presents the numerical simulation setup. The fourth section presents the flow characteristics and the mechanical analysis of the capsule’s threshold of motion. Last, we present the conclusions.

## 2. Physical Experiment

#### 2.1. Wheeled Capsule

#### 2.2. The Experiment System

#### 2.3. Analysis Condition Deployment

## 3. Numerical Simulation

#### 3.1. Simulation Domain Deployment and Mesh

#### 3.2. Turbulence Model

_{i}, u

_{j}are the averaged velocity components, i, j = 1, 2, 3; x

_{i}, x

_{j}are the coordinate components; μ is the dynamic viscosity; p is the pressure; ρu

_{i}u

_{j}is the Reynolds stress; u’

_{i}, u’

_{j}are the fluctuating velocity components; S is the source item.

^{−0.125}; C

_{μ}is the constant number of the model—C

_{μ}= 0.09; l is the reference length of turbulence.

#### 3.3. Verification of Simulation Result

## 4. Result and Discussion

#### 4.1. Total Flow Distribution during Capsule Threshold of Motion

#### 4.2. Different Flow Distributions of the Four Threshold of Motion Conditions

#### 4.2.1. The Axial Velocity Distribution

#### 4.2.2. The Radial Velocity Distribution

#### 4.2.3. The Circular Velocity Distribution

#### 4.3. Theory Analysis

_{1}is the centroid of the outer part, and point C

_{2}is the centroid of the inner part. The external forces acting on the wheeled capsule are the pressure drag force D

_{P}, the friction drag force D

_{F}, and the additional pressure drag force D

_{A}. The friction drag force is the friction force of the water flow acting on the flank of the cylindrical container. The pressure drag force is the pressure difference between the backward surface and the forward surface; its direction is perpendicular to the surface. An additional pressure drag force emerges with the centrifugal effect of the water flow acting on the wheeled capsule in the bent pipe; its direction is radial from the inner bend to the outer bend. At the same time, the friction drag force is always parallel with the wall causing it, so there is no additional friction drag force [16]. The drag forces are fluid dynamical forces and are only related to the shape of the wheeled capsule, so they can be divided into two parts acting on the two centroids individually.

_{A}= 0). Therefore, the drag forces have such an order that the drag force of the inner part’s instability of the bend pipe is minor then the drag force of the outer part’s instability, and the instability of the straight pipe is between them for the same wheeled capsule:

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the physical model of wheeled capsule: (

**a**) physical diagram; (

**b**) schematic diagram.

**Figure 2.**Experiment system: (

**a**) schematic diagram, ①-tank, ②-centrifugal pump, ③-flowmeter, ④-launch device, ⑤-flange, ⑥-straight pipeline, ⑦-wheeled capsule, ⑧-bend pipeline, ⑨-rectangular tank, ⑩-PIV; (

**b**) PIV measuring; (

**c**) bend pipe.

**Figure 3.**Schematic diagram of starting the wheeled capsule at different positions of the bend pipe.

**Figure 4.**Analysis section layout: (

**a**) location θ = 22.5° (first condition); (

**b**) location θ = 67.5° (second condition); (

**c**) location θ = 112.5° (third condition); (

**d**) location θ = 157.5° (fourth condition). The symbols # are the marks of sections; the red lines are the locations of sections; the blue lines are the axis of the pipeline.

**Figure 5.**Grid diagram of each part: (

**a**) mesh of the wheeled capsule; (

**b**) mesh of the interface between the straight and the bend pipes; (

**c**) structured mesh of the straight pipe; (

**d**) unstructured mesh of the bend pipe.

**Figure 6.**Comparison of simulation results and test results of the axial velocity of gap flow: (

**a**) first condition θ = 22.5°; (

**b**) second condition θ = 67.5°; (

**c**) third condition θ = 112.5°; (

**d**) fourth condition θ = 157.5°.

**Figure 7.**The vector diagram of the water flow velocity in the XOZ plane (the horizontal plane where the pipe axis is located), the centroid of the wheeled capsule had angle locations of θ: (

**a**) First condition θ = 22.5°; (

**b**) Second condition θ = 67.5°; (

**c**) Third condition θ = 112.5°; (

**d**) Fourth condition θ = 157.5°.

**Figure 8.**The axial flow velocity distribution cloud map of the characteristic section when the pipeline truck starts at different positions of the pipe bend (the conditions meaning the centroid of the wheeled capsule had angle locations of θ): (

**a**) upstream of the wheeled capsule; (

**b**) gap zone between the capsule and the pipe; (

**c**) downstream of the wheeled capsule.

**Figure 9.**The radial flow velocity distribution cloud map of the characteristic section when the pipeline truck starts at different positions of the pipe bend (the conditions meaning the centroid of the wheeled capsule had angle locations of θ): (

**a**) upstream of the wheeled capsule; (

**b**) gap zone between the capsule and the pipe; (

**c**) downstream of the wheeled capsule.

**Figure 10.**The circumferential flow velocity distribution cloud map of the characteristic section when the pipeline truck starts at different positions of the pipe bend (the conditions meaning the centroid of the wheeled capsule had angle locations of θ): (

**a**) upstream of the wheeled capsule; (

**b**) gap zone between the capsule and the pipe; (

**c**) downstream of the wheeled capsule.

**Figure 11.**The mechanics schematic of wheeled capsule: (

**a**) schematic of the wheeled capsule in straight pipe; (

**b**) schematic of the wheeled capsule in bend pipe; (

**c**) asymmetry force condition of wheeled capsule in bend pipe. The red vectors are the equivalent forces of surface stress; the blue vectors are the concentrate forces.

Experimental Setting | Main Parameter |
---|---|

Illumination | Dual Power Nd-YLF Laser (2 × 30 mJ) |

Camera lens | 2 Imager pro HS cameras |

Image dimension | 2016 × 2016 pixels |

Interrogation area | 32 × 32 pixels |

Time between pulses | 5 × 10^{3} μs |

Seeding material | Polystyrene particles diameter 55 μm |

Resolution ratio | 39.68 μm/pixel |

Condition | Reynolds Number |
---|---|

Straight pipe | 60,840 |

Condition 1 (bend pipe) | 59,350 |

Condition 2 (bend pipe) | 56,108 |

Condition 3 (bend pipe) | 56,950 |

Condition 4 (bend pipe) | 59,593 |

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## Share and Cite

**MDPI and ACS Style**

Lu, Y.; Zhao, Y.; Yuan, Y.; Tian, Y.; Sun, X. Wheeled Capsule Threshold of Motion at Different Locations in a Horizontal Bend Pipeline Based on Hydraulic Capsule Pipeline Transportation. *Water* **2022**, *14*, 3392.
https://doi.org/10.3390/w14213392

**AMA Style**

Lu Y, Zhao Y, Yuan Y, Tian Y, Sun X. Wheeled Capsule Threshold of Motion at Different Locations in a Horizontal Bend Pipeline Based on Hydraulic Capsule Pipeline Transportation. *Water*. 2022; 14(21):3392.
https://doi.org/10.3390/w14213392

**Chicago/Turabian Style**

Lu, Yifan, Yiming Zhao, Yuan Yuan, Yu Tian, and Xihuan Sun. 2022. "Wheeled Capsule Threshold of Motion at Different Locations in a Horizontal Bend Pipeline Based on Hydraulic Capsule Pipeline Transportation" *Water* 14, no. 21: 3392.
https://doi.org/10.3390/w14213392