Numerical Study on the Hydrodynamic Coefficients and Flow Field Characteristics of Underwater Manipulator

Document Type : Regular Article


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

2 Bei qi Foton Motor Co., Ltd., Weifang, 262200, China

3 Zibo Non-public Sector Development Center, Zibo, 255000, China



The hydrodynamic coefficient of an underwater manipulator varies with changes in posture and flow field, presenting significant challenges for precise control and localization. This study, conducted numerical simulations to investigate the patterns of variation in flow field and hydrodynamic coefficients. Results showed that hydrodynamic performance remained consistent when the posture of the manipulator was either axisymmetric or origin-symmetric. Upon rotation, axial flow extended across the entire downstream surface, and the Karman vortex street entirely eliminated. Pressure coefficients on the back pressure surface of the manipulator increased with the Reynolds number within the range of 6×103Re ≤ 3×104, while the pressure coefficient on the upstream surface remained unchanged. Within this range, drag coefficients for the upper and lower arms decreased by 27.4% and 23.9%, respectively. The hydrodynamic performance of the lower arm was independent of the upper arm's posture, with a maximum drag coefficient of 1.48 achieved at α = −90°. As the posture angle of the manipulator varied from 30° to 60°, the pressure coefficient on the upstream surface decreased from 0.75 to 0.25.


Main Subjects

Alzabari, F., Wilson, C. A., & Ouro, P. (2023). Unsteady vortex shedding dynamics behind a circular cylinder in very shallow free-surface flows. Computers & Fluids, 260, 105918.
Avila, J. P. J., Maruyama, N., & Adamowski, J. C. (2008). Hydrodynamic parameter estimation of an open frame unmanned underwater vehicle. IFAC Proceedings Volumes, 41(2), 10504-10509.
Cakir, E., Akinturk, A., & Allievi, A. (2015, May -June). A numerical study of fluid structure interaction of a flexible submerged cylinder mounted on an experimental rig. Proceedings of the ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. St. John's, Newfoundland, Canada.
Carlucho, I., Stephens, D. W., & Barbalata, C. (2021). An adaptive data-driven controller for underwater manipulators with variable payload. Applied Ocean Research, 113, 102726.
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.
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.
Duan, D., Cheng, Y., Liu, X., Yang, X., Zhang, H., & Han, Q. (2023a). Study on the effect of inflow direction on the hydrodynamic characteristics of underwater manipulators. Ocean Engineering, 284, 115221.
Duan, D., Ren, S., Zhang, Y., Cheng, Y., Wang, X., & Zhang, H. (2023b). Hydrodynamic coefficients for various postures of the underwater manipulator. Journal of Applied Fluid Mechanics, 17(2), 461-473.
Franzini, G. R., Fujarra, A. L. C., Meneghini, J. R., Korkischko, I., & Franciss, R. (2009). Experimental investigation of vortex-induced vibration on rigid, smooth and inclined cylinders. Journal of Fluids and Structures, 25(4), 742-750.
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.
Gao, Y., He, J., Ong, M. C., Zhao, M., & Wang, L. (2021). Three-dimensional numerical investigation on flow past two side-by-side curved cylinders. Ocean Engineering, 234, 109167.
He, S., & Seddighi, M. (2013). Turbulence in transient channel flow. Journal of Fluid Mechanics, 715, 60-102.
He, S., & Seddighi, M. (2014). Transition of transient channel flow after a change in Reynolds number. Journal of Fluid Mechanics, 764, 395-427.
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 Engineering and Industrial Aerodynamics, 65(1-3), 335-346.
Hu, G., Tse, K. T., & Kwok, K. C. (2016). Aerodynamic mechanisms of galloping of an inclined square cylinder. Journal of Wind Engineering and Industrial Aerodynamics, 148, 6-17.
Jung, S. Y., & Chung Y. M. (2012) Large-eddy simulation of accelerated turbulent flow in a pipe. International Journal of Heat and Fluid Flow, 33(1), 1-8.
Kawamura, T., Mayer, S., Garapon, A., & Sørensen, L., (2002). Large eddy simulation of a flow past a free surface piercing circular cylinder. Journal of Fluids Engineering, 124(1), 91-101.
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.
Kolodziejczyk, W. (2015). Preliminary study of hydrodynamic load on an underwater robotic manipulator. Journal of Automation Mobile Robots and Intelligent Systems, 9.
Kolodziejczyk, 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.
Kolodziejczyk, W. (2018). The method of determination of transient hydrodynamic coefficients for a single DOF underwater manipulator. Ocean Engineering, 153, 122-131.
Kolodziejczyk, W., Kolodziejczyk, M., Kuzmierowski, T., & Ostaszewski, M. (2023). Transient hydrodynamic coefficient for a single DOF underwater manipulator of square cross-section. Ocean Engineering, 268, 113438.
Liang, S. Z., Zhou, J. W., & Mei, L. (2021). Experiments and numerical simulations of the three-dimensional flow around a finite-length circular cylinder. Ship Science and Technology, 43(11), 19-24.
Liu, P., Shen, D., Ba, Y., Cao, J., Liu, J., & Wang, L., (2022). Development and control strategy of subsea all-electric actuators. Journal of Ocean University of China, 21(5), 1133-1146.
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.
Menter, F. (1993, July). Zonal two equation k-ω turbulence models for aerodynamic flows. 23rd Fluid Dynamic, Plasmadynamics, and Lasers Conference. Orlando, Florida, USA.
Okamoto, T., & Yagita, M. (1973). The experimental investigation on the flow past a circular cylinder of finite length placed normal to the plane surface in a uniform stream. Bulletin of JSME, 16(95), 805-814.
Park, C. W., & Lee, S. J. (2000). Free end effects on the near wake flow structure behind a finite circular cylinder. Journal of Wind Engineering and Industrial Aerodynamics, 88(2-3), 231-246.
Park, C. W., & Lee, S. J. (2004). Effects of free-end corner shape on flow structure around a finite cylinder. Journal of Fluids and Structures, 19(2), 141-158.
PasandidehFard, M., & Naeimirad, M. (2022). Turbulence transient boundary layer over a flat plate. Ocean Engineering, 244, 110192.
Pattenden, R. J., Bressloff, N. W., Turnock, S. R., & Zhang, X., (2007). Unsteady simulations of the flow around a short surface‐mounted cylinder. International Journal for Numerical Methods in Fluids, 53(6), 895-914.
Roh, S. C., & Park, S. (2003). Vortical flow over the free end surface of a finite circular cylinder mounted on a flat plate. Experiments in Fluids, 34(1), 63-67.
Schjølberg, I., & Egeland, O. (1995). Motion control of underwater vehicle-manipulator systems using feedback linearization. IFAC Proceedings Volumes. 28(2), 54-59.
Sumner, D. (2013). Flow above the free end of a surface-mounted finite-height circular cylinder: A review. Journal of Fluids and Structures, 43, 41-63.
Sumner, D., & Heseltine, J. L. (2008). Tip vortex structure for a circular cylinder with a free end. Journal of Wind Engineering and Industrial Aerodynamics. 96(6-7), 1185-1196.
Suzuki, H., Sakaguchi, J., Inoue, T., Watanabe, Y., & Yoshida, H. (2013). Evaluation of methods to estimate hydrodynamic force coefficients of underwater vehicle based on CFD. IFAC Proceedings Volumes, 46(33), 197-202.
Tsukrov, I., Drach, A., DeCew, J., Swift, M. R., & Celikkol, B. (2011). Characterization of geometry and normal drag coefficients of copper nets. Ocean Engineering, 38(17-18), 1979-1988.
Vakil, A., & Green, S. I. (2009). Drag and lift coefficients of inclined finite circular cylinders at moderate Reynolds numbers. Computers & Fluids, 38(9), 1771-1781.
Xu, S., Wu, J., Yang, X., & Zhang, S. (2021). Trajectory tracking and hydrodynamics of a tethered underwater vehicle based on hybrid grid. Ocean Engineering, 241, 110051.
Wang, R., Xin, D., & Ou, J. (2020). Three-dimensional characteristics and axial flow pattern in the wake flow of an oblique circular cylinder. Journal of Wind Engineering and Industrial Aerodynamics, 206, 104381.
Wang, X. C., Gui, H. B., & Liu, Y. (2018). Numerical simulation of three-dimensional flow around a circular cylinder of finite length. Chinese Journal of Ship Research, 13(02), 27-34.
Wang, X., Huang, Q., & Pan, G. (2021). Numerical research on the influence of sail leading edge shapes on the hydrodynamic noise of a submarine. Applied Ocean Research, 117, 102935.
Wu, Y., Ta, X., Xiao, R., Wei, Y., An, D., & Li, D. (2019). Survey of underwater robot positioning navigation. Applied Ocean Research, 90, 101845.
Yu, H., & Thé, J. (2016). Validation and optimization of SST k-ω turbulence model for pollutant dispersion within a building array. Atmosphere Environment, 145, 225-238.
Zdravkovich, M. M., Brand, V. P., Mathew, G., & Weston, A. (1989). Flow past short circular cylinders with two free ends. Journal of Fluid Mechanics, 203, 557-575.
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.
Zhang, Z., Ji, C., Chen, W., Hua, Y., & Srinil, N. (2021). Influence of boundary layer thickness and gap ratios on three-dimensional flow characteristics around a circular cylinder in proximity to a bottom plane. Ocean Engineering, 226, 108858.