Hydrodynamic Coefficients for Various Postures of the Underwater Manipulator

Document Type : Regular Article


School of Mechanical Engineering, University of Jinan, Jinan, 250022, China



The hydrodynamic coefficients of underwater manipulators constantly change during their operation. In this study, the hydrodynamic coefficients of an underwater manipulator were calculated using the finite volume method to better explain its hydrodynamic performance. The drag, lift, and moment coefficients and the Strouhal number of an underwater manipulator for different postures were investigated. The results indicated that in each motion range, the coefficients first increase and then decrease.  Meanwhile, when the attitude of the underwater manipulator is axis-symmetric or origin-symmetric, the hydrodynamic coefficients and the Strouhal number obtained are approximately the identical. The drag coefficient, lift coefficient and moment coefficient reach their maximum values of 3.59, 3.29, and 1.78 at angles of 30°, 150°, and 150°, respectively, with minimum values at 90°, 50° and -30°. Furthermore, the leading-edge shape of the underwater manipulator had a significant effect on the hydrodynamic coefficient. Maximum reductions of 44%, 25%, and 50.5% were obtained in the drag, lift, and moment coefficients, respectively, by comparing the semicircular leading edge with the right-angle leading edge. A maximum Strouhal number of 0.219 was obtained when the semicircular leading edge of the underwater manipulator was the upstream surface. This study will provide theoretical guidance to reveal the hydrodynamic performance of the underwater manipulators. It also serves as a reference for the structural design of the underwater manipulators.


Main Subjects

Ajith, K. R., Arunkumar, K., & Hariprasad, C. M. (2015). Effect of dissimilar leading edges on the flow structures around a square cylinder. Journal of Pressure Vessel Technology, 137(6). https://doi.org/10.1115/1.4029656
Bi, J., Yu, H., & Ren, H. (2012). Two dimensional numerical simulation of flow over a static square cylinder and a static circular cylinder. Journal of China Three Gorges University (Natural Sciences), 34(1), 41-45. https://doi.org/10.3969/j.issn.1672-948X.2012.01.010
Cakir, E., Akinturk, A., & Allievi, A. (2015, May). A numerical study of fluid structure interaction of a flexible submerged cylinder mounted on an experimental rig. International Conference on Offshore Mechanics and Arctic Engineering. American Society of Mechanical Engineers. https://doi.org/10.1115/OMAE2015-42219
Cheng, Y., Duan, D., Liu, X., Yang, X., Zhang, H., & Han, Q. (2022). Numerical study on hydrodynamic performance of underwater manipulator in the subcritical region. Ocean Engineering, 262, 112214. https://doi.org/10.1016/j.oceaneng.2022.112214
Chen, H. L., Dai, S. S., Li, J., & Yao, X. L. (2009). Three-dimensional numerical simulation of the flow past a circular cylinder based on LES method. Journal of Marine Science and Application, 2(8), 110-116. https://doi.org/10.1007/s11804-009-8110-4
Chen, J. M., & Liu, C. H. (1999). Vortex shedding and surface pressures on a square cylinder at incidence to a uniform air stream. International Journal of Heat and Fluid Flow, 20(6), 592-597. https://doi.org/10.1016/S0142-727X(99)00047-8
Chae, J., Yeu, T., Lee, Y., Lee, Y., & Yoon, S. M. (2020). Trajectory tracking performance analysis of underwater manipulator for autonomous manipulation. Journal of Ocean Engineering and Technology, 34(3), 180-193. https://doi.org/10.26748/KSOE.2019.092
Du, Q., Mao, H. Y., & Li, Y. J. (2017) Hydrodynamic characteristics and numerical simulation of flow around square cylinders at different filleting radii. Marine Sciences. 41(07), 137-142. https://doi.org/10.11759/hykx20161120001
Fan, S. B., Lian, L., & Ren, P. (2012). Research on hydrodynamics model test for deepsea open-framed remotely operated vehicle. China Ocean Engineering, 26(2), 329-339. https://doi.org/10.1007/s13344-012-0025-1
Fu, M. Y., Wang, S. S., & Wang, Y. H. (2019). Multi-behavior fusion based potential field method for path planning of unmanned surface vessel. China Ocean Engineering, 3(5), 583-592. https://doi.org/10.1007/s13344-019-0056-y
Gao, W., Nelias, D., Liu, Z., & Lyu, Y. (2018). Numerical investigation of flow around one finite circular cylinder with two free ends. Ocean Engineering, 156, 373-380. https://doi.org/10.1016/j.oceaneng.2018.03.020
Hölscher, N., & Niemann, H. J. (1996). Turbulence and separation induced pressure fluctuations on a finite circular cylinder—application of a linear unsteady strip theory. Journal of Wind Engineering and Industrial Aerodynamics, 65(1-3), 335-346. https://doi.org/10.1016/S0167-6105(97)00051-2.
He, S., & Seddighi, M. (2013). Turbulence in transient channel flow. Journal of Fluid Mechanics, 715, 60-102. https://doi.org/10.1017/jfm.2012.498.
Irwin, R. P., & Chauvet, C. (2007, June). Quantifying hydrodynamic coefficients of complex structures. OCEANS 2007-Europe, IEEE. https://doi.org/10.1109/OCEANSE.2007.4302443
Kolodziejczyk, W. (2015). Preliminary study of hydrodynamic load on an underwater robotic manipulator. Journal of Automation Mobile Robotics and Intelligent Systems, 9. https://doi.org/10.14313/JAMRIS_4-2015/28
Kołodziejczyk, W. (2016). Some considerations on an underwater robotic manipulator subjected to the environmental disturbances caused by water current. Acta Mechanica et Automatica, 10(1), 43-49. https://doi.org/10.1515/ama-2016-0008
Kolodziejczyk, W. (2018). The method of determination of transient hydrodynamic coefficients for a single DOF underwater manipulator. Ocean Engineering, 153, 122-131. https://doi.org/10.1016/j.oceaneng.2018.01.090
Kharghani, M., & PasandidehFard, M. (2022). Turbulence structures in accelerated flow over a flat plate with non-zero pressure gradient. Journal of Applied Fluid Mechanics, 15(2), 311-324. https://doi.org/10.47176/JAFM.15.02.32337
Lyn, D. A., Einav, S., Rodi, W., & Park, J. H. (1995). A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder. Journal of Fluid Mechanics, 304, 285-319. https://doi.org/10.1017/S0022112095004435.
Mathur, A., Gorji, S., He, S., Seddighi, M., Vardy, A., O’Donoghue, T., & Pokrajac, D. (2018). Temporal acceleration of a turbulent channel flow. Journal of Fluid Mechanics, 835, 471-490. https://doi.org/10.1017/jfm.2017.753.
McLain, T. W., & Rock, S. M. (1998). Development and experimental validation of an underwater manipulator hydrodynamic model. The International Journal of Robotics Research, 17(7), 748-759. https://doi.org/10.1177/027836499801700705.
Norberg, C. (1993). Flow around rectangular cylinders: pressure forces and wake frequencies. Journal of Wind Engineering and Industrial Aerodynamics, 49(1-3), 187-196. https://doi.org/10.1016/0167-6105(93)90014-F
PasandidehFard, M., & Naeimirad, M. (2022). Turbulent transient boundary layer over a flat plate. Ocean Engineering, 244, 110192.
Qu, S., Liu, S. N., & Ong, M. C. (2021). An evaluation of different RANS turbulence models for simulating breaking waves past a vertical cylinder. Ocean Engineering, 234, 109195.
Racine, B., & Paterson, E. (2005, June). CFD-based method for simulation of marine-vehicle maneuvering. 35th AIAA Fluid Dynamics Conference and Exhibit. https://doi.org/10.2514/6.2005-4904
Solliec, C., & Danbon, F. (1999). Aerodynamic torque acting on a butterfly valve. comparison and choice of a torque coefficient. https://doi.org/10.1115/1.2823555
Safari, F., Rafeeyan, M., & Danesh, M. (2022). Estimation of hydrodynamic coefficients and simplification of the depth model of an AUV using CFD and sensitivity analysis. Ocean Engineering, 263, 112369. https://doi.org/10.1016/j.oceaneng.2022.112369
Wang, X., Jia, Y. Y., Zheng, Y. F., & Fu, S. F. (2021, September). Numerical simulation of flow around a quasi-square column with Re=6.8×104. Proceedings of the 30th National Conference on structural Eng. https://doi.org/10.26914/c.cnkihy.2021.019108
Wang, H., Meng, Q., & Wang, L., (2007). Analysis on finger dynamics of dexterous underwater hand based on strip theory. Robot, 29(2), 160-166. https://doi.org/10.13973/j.cnki.robot.2007.02.012
Wan, D. C., Shen, Z. R., & Ma, J. (2010). Numerical simulations of viscous flows around surface ship by level set method. Journal of Hydrodynamics, 22(1), 271-277. https://doi.org/10.1016/S1001-6058(09)60206-7
Xu, G., Shen, X., & Yu, K. (2013). Modeling and hydrodynamic performance for a deep ocean manipulator based on numerical approach. Journal of Computers, 8(5), 1192-1199. https://doi.org/10.4304/jcp.8.5.1192-1199
Zhao, M., Cheng, L., & Zhou, T. (2009). Direct numerical simulation of three-dimensional flow past a yawed circular cylinder of infinite length. Journal of Fluids and Structures, 25(5), 831-847. https://doi.org/10.1016/j.jfluidstructs.2009.02.004
Zhang, M., Liu, X., & Tian, Y. (2019). Modeling analysis and simulation of viscous hydrodynamic model of single-DOF manipulator. Journal of Marine Science and Engineering, 7(8), 261. https://doi.org/10.3390/jmse7080261
Zhang, X. S., Wang, J. H., & Wan, D. C. (2020). Numerical techniques for coupling hydrodynamic problems in ship and ocean engineering. Journal of Hydrodynamics, 32, 212-233. https://doi.org/10.1007/s42241-020-0021-5