Numerical Research of the Water Entry of Hyperelastic Spheres Within Low Froude Numbers

Document Type : Regular Article

Authors

National-Provincial Joint Engineering Laboratory for Fluid Transmission System Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China

10.47176/jafm.18.3.2558

Abstract

The water-entry process of solid and hollow hyperelastic spheres was numerically simulated using the arbitrary Lagrange–Euler method, based on the finite element analysis software LS-DYNA. The effect of the different initial velocities on the cavity evolution and deformation of the sphere in a range of low Froude (Fr) numbers was investigated. The evolution of the cavity, deformation of the hyperelastic sphere and parameters at the time of cavity closure were analysed. In addition, the difference in the water-entry process between solid and hollow spheres was given. The numerical results shows that the size of the cavity, fluctuation on the cavity profile, closure time and closure depth increased with Fr and that the closure time was proportional to Fr1/2 for both solid and hollow spheres. However, the relationship between the closure depth and Fr of the hollow sphere differed from that of the solid one. Within the investigated low Froude numbers, whether for the solid or hollow spheres, the deformation amplitude increased with the Froude number. However, the deformation period remained nearly the same for different conditions. Under the same physical and motion parameters, the hollow sphere exhibited larger deformations compared with the solid sphere. The deformation period for the hollow sphere was also longer than that for the solid one.

Keywords

Main Subjects

References

Abeyaratne, R., & Horgan, C. O. (1985). Initiation of localized plane deformations at a circular cavity in an infinite compressible nonlinearly elastic medium. Journal of Elasticity, 15, 243–256. https://doi.org/10.1007/bf00041423
Aquelet, N., & Souli, M. (2004, 25 July). Fluid-structure coupling in a water-wedge impact problem. [ASME/JSME 2004 Pressure Vessels and Piping Conference–San Diego, California, USA]. Emerging Technology in Fluids, Structures, and Fluid Structure Interactions. (pp. 91–99). https://doi.org/10.1115/PVP2004-2887
Aristoff, J. M., & Bush, J. W. (2009). Water entry of small hydrophobic spheres. Journal of Fluid Mechanics, 619, 45–78. https://doi.org/10.1017/s0022112008004382
Aristoff, J. M., Truscott, T. T., Techet, A. H., & Bush, J. W. (2009). The water entry of decelerating spheres. Physics of Fluids, 22, 032102. https://doi.org/10.1063/1.3309454
Belden, J. L., Hurd, R. C., Jandron, M. A., Bower, A. F., & Truscott, T. T. (2016). Elastic spheres can walk on water. Nature Communications, 7, 10551 https://doi.org/10.1038/ncomms10551
Belden, J. L., Speirs, N. B., Hellum, A. M., Jones, M., Paolero, A. J., & Truscott, T. T. (2023). Water entry of cups and disks. Journal of Fluid Mechanics, 963, A14. https://doi.org/10.1017/jfm.2023.330
Blatz, P. J., & Ko, W. (1962). Application of finite elastic theory to the deformation of rubbery materials. Transactions of The Society of Rheology, 6 (1): 223–252. https://doi.org/10.1122/1.548937
Candy, E. G., Kirk, N. E., & Murrell, P. J. (2000). Airframe water impact analysis. International Journal of Crashworthiness, 5, 51–62. https://doi.org/10.1533/cras.2000.0123
Chabokpour, J., & Azamathulla, H. M. (2022). Numerical simulation of pollution transport and hydrodynamic characteristics through the river confluence using FLOW 3D. Water Supply, 22(10), 7821-7832. https://doi.org/10.2166/ws.2022.237
Chang, B., Croson, M., Straker, L., Gart, S. W., Dove, C., Gerwin, J. A., & Jung, S. (2016). How seabirds plunge-dive without injuries. Proceedings of the National Academy of Sciences, 113(43), 12006–12011. https://doi.org/10.1073/pnas.1608628113
Duclaux, V., Caille, F., Duez, C., Ybert, C., Bocquet, L., & Clanet, C. (2007). Dynamics of transient cavities. Journal of Fluid Mechanics, 591, 1–19. https://doi.org/10.1017/S0022112007007343
Gekle, S., van der Bos, A., Bergmann, R., van der Meer, D., & Lohse, D. (2006). Noncontinuous froude number scaling for the closure depth of a cylindrical cavity. Physical Review Letters, 100(8), 084502. https://doi.org/10.1103/physrevlett.100.084502
Hurd, R. C., Belden, J. L., Jandron, M. A., Tate Fanning, D., Bower, A. F., & Truscott, T. T. (2017). Water entry of deformable spheres. Journal of Fluid Mechanics, 824, 912–930. https://doi.org/10.1038/ncomms10551
Jandron, M. A., Hurd, R. C., Belden, J. L., Bower, A. F., Fennell, W. A., & Truscott, T. T. (2014). Modeling of hyperelastic water-skipping spheres using abaqus/explicit. SIMULIA Community Conference.
Kross, D. A., Kiefling, L. A., Murphy, N. C., & Rawls, E. A. (1983, May 02– May 04). Space Shuttle solid rocket booster initial water impact loads and dynamics-Analysis, tests, and flight experience. [American Institute of Aeronautics and Astronautics 24th Structures, Structural Dynamics and Materials Conference–Lake Tahoe]. 24th Structures, Structural Dynamics and Materials Conference. https://doi.org/10.2514/6.1983-956
Lane, B. A., Harmon, K. A., Goodwin, R. L., Yost, M. J., Shazly, T., & Eberth, J. F. (2018). Constitutive modeling of compressible type-I collagen hydrogels. Medical Engineering & Physics, 53, 39–48. https://doi.org/10.1016/j.medengphy.2018.01.003
Machovsky-Capuska, G. E., Howland, H. C., Raubenheimer, D., Vaughn-Hirshorn, R., Würsig, B., Hauber, M. E., & Katzir, G. (2012). Visual accommodation and active pursuit of prey underwater in a plunge-diving bird: the Australasian gannet. Proceedings of the Royal Society B: Biological Sciences, 279(1745), 4118-4125. https://doi.org/10.1098/rspb.2012.1519
May, A. (1952). Vertical entry of missiles into water. Journal of Applied Physics, 23, 1362–1372. https://doi.org/10.1063/1.1702076
May, A., & Woodhull, J. C. (1948). Drag coefficients of steel spheres entering water vertically. Journal of Applied Physics, 19, 1109–1121. https://doi.org/10.1063/1.1715027
McGehee, J. R., Hathaway, M. E., & Vaughan Jr, V. L. (1959). Water-landing characteristics of a reentry capsule (No. NASA-MEMO-5-23-59L).
Mohammadpour, R., Ghani, A. A., & Azamathulla, H. M. (2013). Numerical modeling of 3-D flow on porous broad crested weirs. Applied Mathematical Modelling, 37(22), 9324-9337. https://doi.org/10.1016/j.apm.2013.04.041
Rabbi, R., Speirs, N. B., Kiyama, A., Belden, J. L., & Truscott, T. T. (2020). Impact force reduction by consecutive water entry of spheres. Journal of Fluid Mechanics, 915, A55. https://doi.org/10.1017/jfm.2020.1165
Renda, F., Giorgio-Serchi, F., Boyer, F., & Laschi, C. (2015, May). Locomotion and elastodynamics model of an underwater shell-like soft robot. 2015 IEEE International Conference on Robotics and Automation (ICRA) (pp. 1158-1165). IEEE.
Ropert-Coudert, Y., Grémillet, D., Ryan, P., Kato, A., Naito, Y., & Le Maho, Y. (2004). Between air and water: the plunge dive of the Cape Gannet Morus capensis. Ibis, 146(2), 281-290. https://doi.org/10.1111/j.1474-919x.2003.00250.x
Seddon, C. M., & Moatamedi, M. (2006). Review of water entry with applications to aerospace structures. International Journal of Impact Engineering, 32, 1045–1067. https://doi.org/10.1016/j.ijimpeng.2004.09.002
Souli, M., Messahel, R., Cohen, B., & Aquelet, N. (2014). LS-DYNA Users conference session: fluid structure interaction 1-1 numerical investigation of phase change and cavitation effects in nuclear power plant pipes. Engineering, Environmental Science, Physics.
Speirs, N. B., Langley, K. R., Pan, Z., Truscott, T. T., & Thoroddsen, S. T. (2021). Cavitation upon low-speed solid–liquid impact. Nature Communications, 12, 7250. https://doi.org/10.1038/s41467-021-27383-5
Tang, B., Xu, J., Jia, Y., & Yu, J. (2017). Short fiber-reinforced EPDM coating film superelastic constitutive model. Chinese Journal of Mechanics, 49(2), 317-323. https://doi.org/10.6052/0459-1879-16-324 
Tang, Z., Luo, Q., Leng, X., Liu, P., & Luo, J. (2016). Surge detecting with a spherical sensor. Sensor Review, 36(2), 130-139. https://doi.org/10.1108/SR-12-2014-0765
Techet, A. H., & Truscott, T. T. (2011). Water entry of spinning hydrophobic and hydrophilic spheres. Journal of Fluids and Structures, 27, 716–726. https://doi.org/10.1016/j.jfluidstructs.2011.03.014
Thomas, W. L. (1975). Ditching investigation of a 1/20-scale model of the space shuttle orbiter (No. NASA-CR-2593). NASA.
Thompson, W. C., United States., & Langley Research Center. (1965). Dynamic model investigation of the landing characteristics of a manned spacecraft. Washington, D.C.: National Aeronautics and Space Administration.
Truscott, T. T., Epps, B. P., & Techet, A. H. (2012). Unsteady forces on spheres during free-surface water entry. Journal of Fluid Mechanics, 704, 173–210. https://doi.org/10.1017/jfm.2012.232
Truscott, T.T., Epps, B. P., & Belden, J. L. (2014). Water entry of projectiles. Annual Review of Fluid Mechanics, 46, 355–378. https://doi.org/10.1146/annurev-fluid-011212-140753
Varas, D., Zaera, R., & López-Puente, J. (2009). Numerical modelling of the hydrodynamic ram phenomenon. International Journal of Impact Engineering, 36, 363–374. https://doi.org/10.1016/j.ijimpeng.2008.07.020
Vaughan, V. L., & United States. (1959). Water landing impact accelerations for three models of reentry capsules. Washington, D.C.: National Aeronautics and Space Administration.
Wang, T. M., Yang, X. B., Liang, J. H., Yao, G. C., & Zhao, W. (2013). CFD based investigation on the impact acceleration when a gannet impacts with water during plunge diving. Bioinspiration & Biomimetics, 8.036006. https://doi.org/10.1088/1748-3182/8/3/036006
Wehner, M., Truby, R. L., Fitzgerald, D. J., Mosadegh, B., Whitesides, G. M., Lewis, J. A., & Wood, R. J. (2016). An integrated design and fabrication strategy for entirely soft, autonomous robots. Nature, 536(7617), 451-455. https://doi.org/10.1038/nature19100
Wood, R.W. (1909). A study of splashes. Science, 29, 464–465. https://doi.org/10.1126/science.29.742.464
Xu, L., Troesch, A., & Peterson, R. (1999). Asymmetric hydrodynamic impact and dynamic response of vessels. Journal of Offshore Mechanics and Arctic Engineering-transactions of The Asme, 121, 83–89. https://doi.org/10.1115/1.2830082
Yang, L., Sun, T., Wei, Y., Wang, C., Xia, W., & Wang, Z. (2021a). Hydroelastic analysis of water entry of deformable spheres. Journal of Hydrodynamics, 33, 821–832. https://doi.org/10.1007/s42241-021-0065-1
Yang, L., Wei, Y., Wang, C., Xia, W., & Li, J. (2020a). Numerical investigations on the deformation styles and stress distributions of hyperelastic/viscoelastic spheres during water entry. Journal of Applied Physics, 127(6), 064901. https://doi.org/10.1063/1.5130069
Yang, L., Wei, Y., Wang, C., Xia, W., Li, J., & Chen, C. (2020b). Numerical study on the deformation behaviors of elastic spheres during water entry. Journal of Fluids and Structures, 99, 103167. https://doi.org/10.1016/j.jfluidstructs.2020.103167
Yang, L., Wei, Y., Wang, C., Xia, W., Li, J., Wang, Z., & Zhang, D. (2021b). Dynamics of the cavity evolution during vertical water entry of deformable spheres. Physics of Fluids, 33, 065106. https://doi.org/10.1063/5.0051401
Zhang, L., Wang, Z., & Jia, H. (2023). Effect of wave phases and heights on supercavitation flow field and dynamic characteristics of successively fired high-speed projectiles. Journal of Marine Science and Engineering, 11, 629. (1–17). https://doi.org/10.3390/jmse11030629

Files

History

  • Received: 01 January 2024
  • Revised: 01 September 2024
  • Accepted: 26 September 2024
  • Available online: 01 January 2025

Share

How to cite

Statistics