Abstract
The strong nonlinear interactions between underwater explosion and water surface were numerically investigated using a phase transition model based on a four-equation system, which can deal with the complex deformable interface among different phases, including water, air, explosion bubble, and cavitation. The numerical method is verified by comparing the numerical results with experimental results, and good agreements are found. This study considers an ideal sine wave for simulating the shape of water surface. Two examples of different detonation depths of charge are investigated. In each example, the first case is the basic simulation without surface wave, and the other three cases are the simulations with sine waves of different wavelengths. Unique characteristics of the interactions, such as shock wave propagation, explosion bubble expansion, and the generation, development, and collapse of cavitation, are observed in the numerical simulations. By capturing the detailed density and pressure contours during the interaction process, we can better understand the underlying mechanisms of the explosion bubble, cavitation, and surface waves. These numerical results demonstrate that geometric nonlinearity impacts cavitation evolution and the explosion bubble movement mechanism. Additionally, the secondary cavitation phenomenon has been found in the cases without surface wave, and its fundamental physical mechanism is presented in detail. The present results can expand the existing database of multiphase flow in the underwater explosion and provide an insight into the strong nonlinear interaction between the underwater explosion and water surface.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Cole R. H. Underwater explosion [M]. Princeton City, USA: Princeton University Press, 1948.
Liu J. H. Theory and its applications of ship dynamic responses to non-contact underwater explosions [D]. Doctor Thesis, Wuxi, China: China Ship Scientific Research Center, 2002(in Chinese).
Esplin J. J. Bulk cavitation extent modeling: An energy-based approach [D]. Doctor Thesis, State College, USA: The Pennsylvania State University, 2016.
Phan T. H., Nguyen V. T., Park W. G. Numerical study on strong nonlinear interactions between spark-generated underwater explosion bubbles and a free surface [J]. International Journal of Heat and Mass Transfer, 2020, 163: 120506.
Wu W., Liu Y. L., Zhang A. M. et al. Numerical investigation on underwater explosion cavitation characteristics near water wave [J]. Ocean Engineering, 2020, 205: 107321.
Pearson A., Cox E., Blake J. R. et al. Bubble interactions near a free surface [J]. Engineering Analysis with Boundary Elements, 2004, 28(4): 295–313.
Wang S., Duan W., Wang Q. The bursting of a toroidal bubble at a free surface [J]. Ocean Engineering, 2015, 109: 611–622.
Liu N. N., Ming F. R., Liu L. T. et al. The dynamic behaviors of a bubble in a confined domain [J]. Ocean Engineering, 2017, 144: 175–190.
Shukla R. K., Pantano C., Freund J. B. An interface capturing method for the simulation of multi-phase compressible flows [J]. Journal of Computational Physics, 2010, 229: 7411–7439.
Yu J., Liu G. Z., Wang J. et al. An effective method for modeling the load of bubble jet in underwater explosion near the wall [J]. Ocean Engineering, 2021, 220: 108408.
Zhang Z. F., Wang C., Wang L. K. et al. Underwater explosion of cylindrical charge near plates: Analysis of pressure characteristics and cavitation effects [J]. International Journal of Impact Engineering, 2018, 121: 91–105.
Jin Z., Yin C., Chen Y. et al. Study on the cavitation effects induced by the interaction between underwater blast and various boundaries [J]. Ocean Engineering, 2021, 222: 108596.
Allaire G., Clerc S., Kokh S. A five-equation model for the simulation of interface between compressible fluids [J]. Journal of Computational Physics, 2002, 181: 577–616.
Kapila A. K., Menikoff R., Bdzil J. B. et al. Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations [J]. Physics of Fluids, 2001, 13(10): 3002–3024.
Mulder W., Osher S., Sethian J. A. Computing interface motion in compressible gas dynamics [J]. Journal of Computational Physics, 1992, 100: 209–228.
Yu J., Liu J. H., He B. et al. Numerical research of water jet characteristics in underwater explosion based on compressible multicomponent flows [J]. Ocean Engineering, 2021, 242: 110135.
Chen Y., Heister S. D. A numerical treatment for attached cavitation [J]. Journal of Fluids Engineering, 1994, 116(3): 613–618.
Tang H. S., Huang D. A second-order accurate capturing scheme for 1D inviscid flows of gas and water with vacuum zones [J]. Journal of Computational Physics, 1996, 128(2): 301–318.
Schmidt D. P., Rutland C. J., Corradini M. L. A fully compressible, two-dimensional model of small, high speed, cavitating nozzles [J]. Atomization and Sprays, 1999, 9(3): 255–276.
Qin J. R., Yu S. T., Lai M. C. Direct calculations of cavitating flows in fuel delivery pipe by the space-time CE/SE method [C]. SAE International Fuels and Lubricants Meeting and Exposition, Copenhagen, Denmark, 1999.
Liu T. G., Khoo B. C., Xie W. F. Isentropic one-fluid modelling of unsteady cavitating flow [J]. Journal of Computational Physics, 2004, 201(1): 80–108.
Xie W. F., Liu T. G., Khoo B. C. Application of a one-fluid model for large scale homogeneous unsteady cavitation: The modified Schmidt model [J]. Computers and Fluids, 2006, 35(10): 1177–1192.
Daramizadeh A., Ansari M. R. Numerical simulation of underwater explosion near air-water free surface using a five-equation reduced model [J]. Ocean Engineering, 2015, 110: 25–35.
Baer M. R., Nunziato J. W. A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials [J]. International Journal of Multiphase Flow, 1986, 12(6): 861–889.
Pelanti M., Shyue K. M. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves [J]. Journal of Computational Physics, 2014, 259: 331–357.
Pelanti M., Shyue K. M. A numerical model for multiphase liquid-vapor-gas flows with interfaces and cavitation [J]. International Journal of Multiphase Flow, 2019, 113: 208–230.
Chiapolino A., Boivin P., Saurel R. A simple phase transition relaxation solver for liquid-vapor flows [J]. International Journal for Numerical Methods in Fluids, 2016, 83(7): 583–605.
Chiapolino A., Boivin P., Saurel R. A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows [J]. Computers and Fluids, 2017, 150: 31–45.
Yu J., Liu J. H., Wang H. K. et al. Numerical simulation of underwater explosion cavitation characteristics based on phase transition model in compressible multicomponent fluids [J]. Ocean Engineering, 2021, 240: 109934.
Yu J., Liu J. H., Wang H. K. et al. Application of two-phase transition model in underwater explosion cavitation based on compressible multiphase flows [J]. AIP Advances, 2022, 12: 025209.
Zhang J. A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows [J]. International Journal of Multiphase Flow, 2020, 132: 103417.
Le Metayer O., Saurel R. The noble-abel stiffened-gas equation of state [J]. Physics of Fluids, 2016, 28(4): 046102.
Cui P., Zhang A. M., Wang S. P. Small-charge underwater explosion bubble experiments under various boundary conditions [J]. Physics of Fluids, 2016, 28(11): 117103.
Acknowledgement
(This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Compliance with ethical standards
Conflict of interest: The authors declare that they have no conflict of interest.
Informed consent: Informed consent was obtained from all individual participants included in the study.
Biography: Jun Yu (1984–), Male, Master, Senior engineer
Rights and permissions
About this article
Cite this article
Yu, J., Wang, Hk., Sheng, Zx. et al. Investigation on strong nonlinear interactions between underwater explosion and water surface based on compressible multiphase flow with phase transition. J Hydrodyn 35, 351–364 (2023). https://doi.org/10.1007/s42241-023-0017-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42241-023-0017-z