# Study on the Adsorption Performance of a Vortex Suction Cup under Varying Diameters of Underwater Structure Tubes

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Vortex Suction Cup and Adsorption Gap

#### 2.1. The Proposed Vortex Suction Cup

_{1}. The height of the impeller is denoted as H, while a deliberate gap labeled H

_{2}exists between the impeller and the lower surface of the chamber to prevent any potential contact or abrasion between them. In terms of an overhead view, there is a folding angle φ present at the outer end of the impeller, with specified dimensions including the impeller radius r

_{1}, inner cavity radius r

_{2}, outer cavity radius r

_{3}, and shell radius r

_{4}. Table 1 provides a detailed list of these specific dimensions.

#### 2.2. The Adsorption Gap of Vortex Suction Cup

_{max}, respectively. This setting establishes the following relationship:

_{max}. The numerical results are illustrated in Figure 4. It is observed that as the radius of wall curvature decreases, the maximum adsorption gap h

_{max}of the vortex suction cup increases. Specifically, for wall curvature radii less than 1000 mm, h

_{max}exhibits a pronounced variation. In contrast, when the wall curvature radius exceeds 1000 mm, the change in the maximum adsorption gap becomes more gradual, with a variation of less than 2.5 mm. Consequently, for subsequent simulation and verification experiments, it is advisable to design a greater number of experimental groups for radii below 1000 mm, whereas fewer groups suffice for wall radii exceeding 1000 mm.

## 3. Computational Fluid Dynamics (CFD) Simulation

#### 3.1. Simulation Setup

#### 3.2. Simulation Flow Field Observation

#### 3.2.1. Flow Velocity Distribution

_{max}, gradually increases, providing a larger channel for velocity and energy exchange between internal and external fluids. More fluid beneath the suction cup is also driven into rotation.

#### 3.2.2. Pressure Distribution

## 4. Experimental Validation and Discussion

#### 4.1. Setup for the Experiment

#### 4.2. Results and Discussions

#### 4.2.1. Comparison of Experimental and Simulation Results

_{F}) can be determined using the following calculation:

_{sim}represents the simulation force and F

_{exp}represents the experimental force. The torque relative error δ

_{T}can be calculated using Equation (3) by substituting T

_{sim}and T

_{exp}, which represent the simulated torque and experimental torque, respectively. The results associated with each data point are depicted in Figure 11. The force and torque exhibit maximum relative errors of 2.29% and 6.25%, respectively, while the adsorption force and torque demonstrate average relative errors of 1.02% and 2.70%. Due to the limitation of the size of the experimental water tank, we observed that the external water flow around the suction cup was affected by high-speed vortices inside the suction cup, resulting in slow movement within the water tank. In simulation, the volume of the simulated domain is much larger than the actual volume of the water tank, which may be one potential reason for discrepancies between experimental and simulated results. Overall, these errors fall within an acceptable range, indicating that the CFD simulation adequately represents this complex problem.

#### 4.2.2. Adsorption Forces

#### 4.2.3. Required Torque

#### 4.2.4. Power Consumption

#### 4.2.5. Adsorption Efficiency

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Bhattacharyya, S.; Asada, H.H. Control of a Compact, Tetherless ROV for In-Contact Inspection of Complex Underwater Structures. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Chicago, IL, USA, 14–18 September 2014; pp. 2265–2272. [Google Scholar]
- Hirai, H.; Ishii, K. Development of Dam Inspection Underwater Robot. J. Robot. Netw. Artif. Life
**2019**, 6, 18–22. [Google Scholar] [CrossRef] - Sakagami, N.; Yumoto, Y.; Takebayashi, T.; Kawamura, S. Development of dam inspection robot with negative pressure effect plate. J. Field Robot.
**2019**, 36, 1422–1435. [Google Scholar] [CrossRef] - Qin, Y.; Dong, S.; Pang, R.; Xia, Z.; Yang, J. Design and Kinematic Analysis of a Wall-climbing Robot for Bridge appearance Inspection. IOP Conf. Ser. Earth Environ. Sci.
**2021**, 638, 012062. [Google Scholar] [CrossRef] - Iwahori, T.; Takebayashi, T.; Saltagami, N.; Kawainura, S. Computational and Experimental Investigation of a Negative Pressure Effect Plate for Underwater Inspection Robots. In Proceedings of the IEEE/SICE International Symposium on System Integration (SII), Iwaki, Japan, 11–14 January 2021; pp. 239–243. [Google Scholar]
- Yamada, D.; Takebayashi, T.; Kato, H.; Sakagami, N.; Kawamura, S. Underwater Robot with Negative Pressure Effect Plates for Maintenance of Underwater Structures. In Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Hong Kong, China, 8–12 July 2019; pp. 1092–1097. [Google Scholar]
- Souto, D.; Faina, A.; Pea, F.L.; Duro, R.J. Morphologically intelligent underactuated robot for underwater hull cleaning. In Proceedings of the IEEE International Conference on Intelligent Data Acquisition & Advanced Computing Systems: Technology & Applications, Warsaw, Poland, 24–26 September 2015. [Google Scholar]
- Tavakoli, M.; Viegas, C.; Marques, L.; Norberto Pires, J.; de Almeida, A.T. OmniClimbers: Omni-directional magnetic wheeled climbing robots for inspection of ferromagnetic structures. Robot. Auton. Syst.
**2013**, 61, 997–1007. [Google Scholar] [CrossRef] - Fan, J.; Yang, C.; Chen, Y.; Wang, H.; Huang, Z.; Shou, Z.; Jiang, P.; Wei, Q. An underwater robot with self-adaption mechanism for cleaning steel pipes with variable diameters. Ind. Robot-Int. J. Robot. Res. Appl.
**2018**, 45, 193–205. [Google Scholar] [CrossRef] - Yang, P.; Zhang, M.; Sun, L.; Li, X. Design and Control of a Crawler-Type Wall-Climbing Robot System for Measuring Paint Film Thickness of Offshore Wind Turbine Tower. J. Intell. Robot. Syst.
**2022**, 106, 50. [Google Scholar] [CrossRef] - Guan, Y.; Zhu, H.; Wu, W.; Zhou, X.; Jiang, L.; Cai, C.; Zhang, L.; Zhang, H. A Modular Biped Wall-Climbing Robot With High Mobility and Manipulating Function. IEEE-ASME Trans. Mechatron.
**2013**, 18, 1787–1798. [Google Scholar] [CrossRef] - Wang, J.-R.; Xi, Y.-X.; Ji, C.; Zou, J. A biomimetic robot crawling bidirectionally with load inspired by rock-climbing fish. J. Zhejiang Univ. Sci. A
**2022**, 23, 14–26. [Google Scholar] [CrossRef] - Nassiraei, A.A.F.; Sonoda, T.; Ishii, K. Development of Ship Hull Cleaning Underwater Robot. In Proceedings of the Fifth International Conference on Emerging Trends in Engineering & Technology, Himeji, Japan, 5–7 November 2012. [Google Scholar]
- Chen, Y.Z.; Hu, Y.H. Research and Application of Ship Hull Fouling Cleaning Technologies. Surf. Technol.
**2017**, 46, 60–71. [Google Scholar] - Chen, L.; Cui, R.; Yan, W.; Xu, H.; Zhao, H.; Li, H. Design and climbing control of an underwater robot for ship hull cleaning. Ocean Eng.
**2023**, 274, 114024. [Google Scholar] [CrossRef] - Brusell, A.; Andrikopoulos, G.; Nikolakopoulos, G. Novel Considerations on the Negative Pressure Adhesion of Electric Ducted Fans: An Experimental Study. In Proceedings of the 25th Mediterranean Conference on Control and Automation (MED), Valletta, Malta, 3–6 July 2017; pp. 1404–1409. [Google Scholar]
- Chen, Y.; Liu, S.; Zhang, L.; Zheng, P.; Yang, C. Study on the adsorption performance of underwater propeller-driven Bernoulli adsorption device. Ocean Eng.
**2022**, 266, 112724. [Google Scholar] [CrossRef] - Li, X.; Li, N.; Tao, G.; Liu, H.; Kagawa, T. Experimental comparison of Bernoulli gripper and vortex gripper. Int. J. Precis. Eng. Manuf.
**2015**, 16, 2081–2090. [Google Scholar] [CrossRef] - Li, X.; Kagawa, T. Development of a new noncontact gripper using swirl vanes. Robot. Comput. Integr. Manuf.
**2013**, 29, 63–70. [Google Scholar] [CrossRef] - Zhou, Q.; Li, X. Design of wall-climbing robot using electrically activated rotational-flow adsorption unit. In Proceedings of the 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, Republic of Korea, 9–14 October 2016. [Google Scholar]
- Dong, L.J.; Li, X.; Liu, H.; Tao, G.L. Development and Analysis of an Electrically Activated Sucker for Handling Workpieces With Rough and Uneven Surfaces. In Proceedings of the IEEE International Conference on Advanced Intelligent Mechatronics, Busan, Republic of Korea, 7–11 July 2015. [Google Scholar]
- Zhu, Y.; Zhou, R.; Yang, G.; Zhu, Y.; Hu, D. Experimental and numerical study of the adsorption performance of a vortex suction device using water-swirling flow. Sci. China-Technol. Sci.
**2020**, 63, 931–942. [Google Scholar] [CrossRef] - Zhao, Y.B.; Yang, C.J.; Chen, Y.H.; Li, J.; Liu, S.Y.; Ye, G.Y. Study on the Optimal Design for Cavitation Reduction in the Vortex Suction Cup for Underwater Climbing Robot. J. Mar. Sci. Eng.
**2022**, 10, 70. [Google Scholar] [CrossRef] - Fan, S.; Cheng, X.; Qiao, K.; Liu, S.; Xu, W. Optimization design and experimental validation of a vortex-based suction cup for a climbing AUV. Ocean Eng.
**2022**, 257, 111602. [Google Scholar] [CrossRef] - Guo, T.; Liu, X.; Song, D. Innovative sliding negative pressure adsorptive approach applied to an underwater climbing adsorption robot. Phys. Fluids
**2021**, 33, 117107. [Google Scholar] [CrossRef] - Darmawan, S.; Tanujaya, H. CFD Investigation of Flow Over a Backward-Facing Step Using AN RNG k-ε Turbulence Model. Int. J. Technol.
**2019**, 10, 280–289. [Google Scholar] [CrossRef] - Almohammadi, K.M.; Ingham, D.B.; Ma, L.; Pourkashan, M. Computational fluid dynamics (CFD) mesh independency techniques for a straight blade vertical axis wind turbine. Energy
**2013**, 58, 483–493. [Google Scholar] [CrossRef] - Tang, Q.; Du, Y.; Ding, M.; Zhang, S.; Zhao, Q.; Hu, S.; Tian, C.; Wang, L.; Li, Y.; Wang, G. Study on the performance of vortex suction cup for an underwater inspection robot. Ocean Eng.
**2024**, 300, 117462. [Google Scholar] [CrossRef]

**Figure 12.**Adsorption force of suction cups under different curvature radii. (

**a**) Experimental results of adhesion force of vortex suction cups under different curvatures. (

**b**) Adhesion force percentage curve of vortex suction cups under different curvatures.

**Figure 14.**Power consumption of suction cups under different curvature radii. (

**a**) A calculation of the power consumption of vortex suction cups under different curvatures. (

**b**) Power consumption percentage curve of vortex suction cups under different curvatures.

**Figure 15.**Adhesion efficiency of suction cups under different curvature radii. (

**a**) A calculation of the adhesion efficiency of vortex suction cups under different curvatures. (

**b**) Adhesion efficiency percentage curve of vortex suction cups under different curvatures.

H | H_{1} | H_{2} | r | r_{1} | r_{2} | r_{3} | r_{4} | φ |
---|---|---|---|---|---|---|---|---|

10 mm | 1.3 mm | 0.7 mm | 10 mm | 42.3 mm | 58.5 mm | 60 mm | 70 mm | 150° |

Coarse | Medium | Fine | |
---|---|---|---|

Basic size | 0.12 (mm) | 0.1 (mm) | 0.08 (mm) |

Mesh quantity | 764,024 | 1,142,622 | 1,989,966 |

Simulation force | 270 (N) | 270 (N) | 269 (N) |

Simulation torque | 0.88 (Nm) | 0.91 (Nm) | 0.91 (Nm) |

Adsorption Surface Curvature Radius (mm) | Experimental Force (N) | Simulated Force (N) | Experimental Torque (Nm) | Simulation Torque (Nm) |
---|---|---|---|---|

150 | 173 | 173 | 0.56 | 0.54 |

200 | 179 | 175 | 0.49 | 0.49 |

300 | 181 | 180 | 0.45 | 0.48 |

500 | 185 | 182 | 0.48 | 0.48 |

800 | 186 | 186 | 0.47 | 0.46 |

2000 | 187 | 191 | 0.46 | 0.44 |

Flat | 191 | 192 | 0.46 | 0.45 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tang, Q.; Du, Y.; Liu, Z.; Zhang, S.; Zhao, Q.; Li, Y.; Wang, L.; Cui, T.; Wang, G.
Study on the Adsorption Performance of a Vortex Suction Cup under Varying Diameters of Underwater Structure Tubes. *J. Mar. Sci. Eng.* **2024**, *12*, 662.
https://doi.org/10.3390/jmse12040662

**AMA Style**

Tang Q, Du Y, Liu Z, Zhang S, Zhao Q, Li Y, Wang L, Cui T, Wang G.
Study on the Adsorption Performance of a Vortex Suction Cup under Varying Diameters of Underwater Structure Tubes. *Journal of Marine Science and Engineering*. 2024; 12(4):662.
https://doi.org/10.3390/jmse12040662

**Chicago/Turabian Style**

Tang, Qinyun, Ying Du, Zhaojin Liu, Shuo Zhang, Qiang Zhao, Yingxuan Li, Liquan Wang, Tong Cui, and Gang Wang.
2024. "Study on the Adsorption Performance of a Vortex Suction Cup under Varying Diameters of Underwater Structure Tubes" *Journal of Marine Science and Engineering* 12, no. 4: 662.
https://doi.org/10.3390/jmse12040662