Analysis of Horizontal Cylinder Load under Different Conditions in Regards to Waves and Flows
Abstract
:1. Introduction
2. Model Establishment
2.1. Fluid Control Equation
2.2. Establishing a Computational Model
2.3. Grid Convergence Analysis
2.4. Numerical Verification of Wave and Current Forces
2.5. Equation of Cylindrical Motion
2.6. Energy Capture Efficiency
3. Analysis of Calculation Results
3.1. Example Setting and Calculation Parameters
3.2. Load Analysis of Waves and Flows on Fixed Cylinders
3.2.1. Analysis of the Force Acting on a Fixed Cylinder under Different Submergence Depths
3.2.2. Analysis of the Force Acting on a Fixed Cylinder under Different Wave Conditions
3.2.3. Analysis of the Force Acting on a Fixed Cylinder under Different Cylinder Sizes
3.3. Displacement Analysis of Rotating Cylinders by Waves and Flows
3.4. Analysis of the Interaction Flow Field between Waves and Rotating Cylinders
3.5. Analysis of Fluid Load on Rotating Cylinders
3.5.1. Fluid Load Analysis under Different Wave Conditions
3.5.2. Fluid Load Analysis under Different k Values
3.5.3. Fluid Load Analysis under Different Cylinder Radii
3.5.4. Fluid Load Analysis under Different Arm Lengths
3.6. Calculation of Energy Harvesting Efficiency of a Cantilever Cylinder Rotating around an Axis under Wave Current Conditions
4. Conclusions
- (1)
- When a cylinder approaches a free surface, its hydrodynamic load under wave current conditions is more sensitive to changes in submergence depth, which affects wave reflection and wave blockage.
- (2)
- The main frequency of the Fourier transform of the cylindrical motion curve remains unchanged at different flow velocities, k values, force arms, and radii; the main frequency of the Fourier transform of the cylindrical motion curve varies with the wave period and the depth of submergence.
- (3)
- The efficiency of rotary cylindrical energy harvesting is influenced by various factors, among which an initial increase and then decrease are observed with a gradually increasing k value, arm length, period, and radius, in addition to an observed decrease with increasing flow velocity.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Reichl, P.; Hourigan, K.; Thompson, M. The unsteady wake of a circular cylinder near a free surface. Flow Turbul. Combust. 2003, 71, 347–359. [Google Scholar] [CrossRef]
- Reichl, P.; Hourigan, K.; Thompson, M.C. Flow past a cylinder close to a free surface. J. Fluid Mech. 2005, 533, 269–296. [Google Scholar] [CrossRef]
- Wu, C.S.; Young, D.L. Simulations of free-surface flows with an embedded object by a coupling partitioned approach. Comput. Fluids 2014, 89, 66–77. [Google Scholar] [CrossRef]
- Bozkaya, C.; Kocabiyik, S.; Mironova, L.A.; Gubanov, O.I. Streamwise oscillations of a cylinder beneath a free surface: Free surface effects on vortex formation modes. J. Comput. Appl. Math. 2011, 235, 4780–4795. [Google Scholar] [CrossRef]
- Xiao, H.; Huang, W.; Tao, J.; Liu, C. Numerical modeling of wave–current forces acting on horizontal cylinder of marine structures by VOF method. Ocean. Eng. 2013, 67, 58–67. [Google Scholar] [CrossRef]
- Bai, J.; Ma, N.; Gu, X. Numerical study of the interaction between combined wave-current and a horizontal cylinder close to the free surface. In Proceedings of the International Ocean and Polar Engineering Conference, Rhodes, Greece, 26 June–2 July 2016. [Google Scholar]
- Gu, M.; Song, B.; Zhang, B.; Mao, Z.; Tian, W. The effects of submergence depth on Vortex−Induced Vibration (VIV) and energy harvesting of a circular cylinder. Renew. Energy 2020, 151, 931–945. [Google Scholar] [CrossRef]
- Zhao, W.; Wan, D.; Zhao, S. CFD simulation of two-phase flows past a surface-piercing circular cylinder. In Proceedings of the International Ocean and Polar Engineering Conference, Virtual, 11–16 October 2020. [Google Scholar]
- Wang, Y.; Lou, M.; Liu, X. Experimental design of energy capture for cylindrical flow induced vibration under wake interference. Lab. Res. Explor. 2023, 42, 62–65. [Google Scholar]
- Wang, C.; Lv, H.; Huang, J.; Yang, Y. Research on the interaction between second-order wave current and upright double cylinders. J. Huazhong Univ. Sci. Technol. (Nat. Sci. Ed.) 2023, 51, 135–141. [Google Scholar]
- Zhang, X.; Huo, J.; Zhang, M.; Xie, Z. Solitary wave-current forces on a horizontal cylinder by a fourth-order-accurate finite volume compact solver. Ocean. Eng. 2024, 294, 116788. [Google Scholar] [CrossRef]
- Lin, Z.; Zan, X. Numerical study on load characteristics by internal solitary wave on cylinder sections at different depth and its parameterization. Ocean. Eng. 2021, 219, 108343. [Google Scholar] [CrossRef]
- Yang, Z.; Huang, B.; Kang, A.; Zhu, B.; Han, J.; Yin, R.; Li, X. Experimental study on the solitary wave-current interaction and the combined forces on a vertical cylinder. Ocean. Eng. 2021, 236, 109569. [Google Scholar] [CrossRef]
- Zang, Z.; Chen, Z.; Zhao, M.; Xu, W.; Chen, Y. Experimental study on dynamic responses of a tensioned flexible vertical cylinder under waves and combined current and waves. Ocean. Eng. 2022, 266, 113159. [Google Scholar] [CrossRef]
- Xin, Z.; Li, X.; Li, Y. Coupled effects of wave and depth-dependent current interaction on loads on a bottom-fixed vertical slender cylinder. Coast. Eng. 2023, 183, 104304. [Google Scholar] [CrossRef]
- Huo, S.; Deng, S.; Song, Z.; Zhao, W.; Wan, D. On the hydrodynamic response and slamming impact of a cylindrical FPSO in combined wave-current flows. Ocean. Eng. 2023, 275, 114139. [Google Scholar] [CrossRef]
- Ning, D.; Lin, H.; Teng, B.; Zou, Q. Higher harmonics induced by waves propagating over a submerged obstacle in the presence of uniform current. China Ocean. Eng. 2014, 28, 725–738. [Google Scholar] [CrossRef]
- Saincher, S.; Sriram, V.; Agarwal, S.; Schlurmann, T. Experimental investigation of hydrodynamic loading induced by regular, steep non-breaking and breaking focused waves on a fixed and moving cylinder. Eur. J. Mech. -B/Fluids 2022, 93, 42–64. [Google Scholar] [CrossRef]
- Zhou, X.; Jiang, Q.; Wang, Y.; Chen, L.; Wang, S.; Wang, K. Numerical Simulation of Wave–Current Force Characteristics of Horizontal Floating Cylinder in Heave Motion. J. Mar. Sci. Eng. 2022, 10, 1884. [Google Scholar] [CrossRef]
- Belloli, M.; Giappino, S.; Morganti, S.; Muggiasca, S.; Zasso, A. Vortex induced vibrations at high Reynolds numbers on circular cylinders. Ocean. Eng. 2015, 94, 140–154. [Google Scholar] [CrossRef]
- Dhanwani, M.A.; Sarkar, A.; Patnaik, B.S.V. Lumped parameter models of vortex induced vibration with application to the design of aquatic energy harvester. J. Fluids Struct. 2013, 43, 302–324. [Google Scholar] [CrossRef]
- Sirohi, J.; Mahadik, R. Harvesting wind energy using a galloping piezoelectric beam. J. Vib. Acoust. 2012, 134, 11009. [Google Scholar] [CrossRef]
- Abdelkefi, A.; Yan, Z.; Hajj, M.R. Modeling and nonlinear analysis of piezoelectric energy harvesting from transverse galloping. Smart Mater. Struct. 2013, 22, 025016. [Google Scholar] [CrossRef]
- Bai, J.; Ma, N.; Gu, X. Wave-current loads on the horizontal cylinder with varying submergence depths. J. Shanghai Jiao Tong Univ. 2018, 52, 938–945. [Google Scholar]
- Banaszek, A.; Petrovic, R.; Zyliński, B. FEM analysis of pipe material temperature changes influence on line expansion loops in hydraulic installations on modern tankers. Therm. Sci. 2011, 15, 81–90. [Google Scholar] [CrossRef]
Grid | Number of Grids within the Wavelength Range | Number of Grids within the Wave Height Range | Total Number of Two-Dimensional Grids |
---|---|---|---|
1 | 80 | 15 | 1.82 × 105 |
2 | 100 | 20 | 2.28 × 105 |
3 | 120 | 25 | 2.72 × 105 |
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
Zhou, X.; Jiang, Q.; Wang, K.; Wang, S. Analysis of Horizontal Cylinder Load under Different Conditions in Regards to Waves and Flows. J. Mar. Sci. Eng. 2024, 12, 1101. https://doi.org/10.3390/jmse12071101
Zhou X, Jiang Q, Wang K, Wang S. Analysis of Horizontal Cylinder Load under Different Conditions in Regards to Waves and Flows. Journal of Marine Science and Engineering. 2024; 12(7):1101. https://doi.org/10.3390/jmse12071101
Chicago/Turabian StyleZhou, Xiaoguo, Qingdian Jiang, Kai Wang, and Shuqi Wang. 2024. "Analysis of Horizontal Cylinder Load under Different Conditions in Regards to Waves and Flows" Journal of Marine Science and Engineering 12, no. 7: 1101. https://doi.org/10.3390/jmse12071101