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SPH-BEM simulation of underwater explosion and bubble dynamics near rigid wall

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Abstract

A process of underwater explosion of a charge near a rigid wall includes three main stages: charge detonation, bubble pulsation and jet formation. A smoothed particle hydrodynamics (SPH) method has natural advantages in solving problems with large deformations and is suitable for simulation of processes of charge detonation and jet formation. On the other hand, a boundary element method (BEM) is highly efficient for modelling of the bubble pulsation process. In this paper, a hybrid algorithm, fully utilizing advantages of both SPH and BEM, was applied to simulate the entire process of free and near-field underwater explosions. First, a numerical model of the free-field underwater explosion was developed, and the entire explosion process–from the charge detonation to the jet formation–was analysed. Second, the obtained numerical results were compared with the original experimental data in order to verify the validity of the presented method. Third, a SPH model of underwater explosion for a column charge near a rigid wall was developed to simulate the detonation process. The results for propagation of a shock wave are in good accordance with the physical observations. After that, the SPH results were employed as initial conditions for the BEM to simulate the bubble pulsation. The obtained numerical results show that the bubble expanded at first and then shrunk due to a differences of pressure levels inside and outside it. Here, a good agreement between the numerical and experimental results for the shapes, the maximum radius and the movement of the bubble proved the effectiveness of the developed numerical model. Finally, the BEM results for a stage when an initial jet was formed were used as initial conditions for the SPH method to simulate the process of jet formation and its impact on the rigid wall. The numerical results agreed well with the experimental data, verifying the feasibility and suitability of the hybrid algorithm. Besides, the results show that, due to the effect of the Bjerknes force, a jet with a high speed was formed that may cause local damage to underwater structures.

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References

  1. Hu J, Chen Z Y, Zhang X D, et al. Underwater explosion in centrifuge. Part I: Validation and calibration of scaling laws. Sci China Tech Sci, 2017, 60: 1638–1657

    Google Scholar 

  2. Yuan L, Zhou H Y, Liang X Q, et al. Underwater explosion in centrifuge. Part II: Dynamic responses of defensive steel plate. Sci China Tech Sci, 2017, 60: 1941–1957

    Google Scholar 

  3. Zhang Z, Wang L, Silberschmidt V V. Damage response of steel plate to underwater explosion: Effect of shaped charge liner. Int J Impact Eng, 2017, 103: 38–49

    Article  Google Scholar 

  4. Cui P, Zhang A M, Wang S P, et al. Ice breaking by a collapsing bubble. J Fluid Mech, 2018, 841: 287–309

    Article  Google Scholar 

  5. Zhang A M, Yang W S, Huang C, et al. Numerical simulation of column charge underwater explosion based on SPH and BEM combination. Comput Fluids, 2013, 71: 169–178

    Article  MathSciNet  MATH  Google Scholar 

  6. Snay H G. Underwater Explosion Phenomena: The Parameters of Migrating Bubbles. NAVORD Report. 1962

    Google Scholar 

  7. Snay H G, Tipton R V. Charts for the Parameters of Migrating Explosion Bubbles. NAVORD Report. 1962

    Google Scholar 

  8. Klaseboer E, Hung K C, Wang C, et al. Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure. J Fluid Mech, 2005, 537: 387–413

    Article  MATH  Google Scholar 

  9. Zhu X, Mu J L, Hong J B, et al. Experimental study of characters of bubble impulsion induced by underwater explosions. J Harbin Eng Univ, 2007, 28: 365–368

    Google Scholar 

  10. Wang H, Zhu X, Cheng Y S, et al. Experimental and numerical investigation of ship structure subjected to close-in underwater shock wave and following gas bubble pulse. Mar Struct, 2014, 39: 90–117

    Article  Google Scholar 

  11. Chen Y, Tong Z P, Hua H X, et al. Experimental investigation on the dynamic response of scaled ship model with rubber sandwich coatings subjected to underwater explosion. Int J Impact Eng, 2009, 36: 318–328

    Article  Google Scholar 

  12. Hung C F, Hwangfu J J. Experimental study of the behaviour of minicharge underwater explosion bubbles near different boundaries. J Fluid Mech, 2010, 651: 55–80

    Article  MATH  Google Scholar 

  13. Gong S W, Ohl S W, Klaseboer E, et al. Scaling law for bubbles induced by different external sources: Theoretical and experimental study. Phys Rev E, 2010, 81: 056317

    Article  Google Scholar 

  14. Li J, Rong J L. Experimental and numerical investigation of the dynamic response of structures subjected to underwater explosion. Eur J Mech - B/Fluids, 2012, 32: 59–69

    Article  MATH  Google Scholar 

  15. Zhang A M, Cui P, Cui J, et al. Experimental study on bubble dynamics subject to buoyancy. J Fluid Mech, 2015, 776: 137–160

    Article  Google Scholar 

  16. Cui P, Zhang A M, Wang S P. Small-charge underwater explosion bubble experiments under various boundary conditions. Phys Fluids, 2016, 28: 117103

    Article  Google Scholar 

  17. Park J. A coupled runge kutta discontinuous Galerkin-direct ghost fluid (RKDG-DGF) method to near-field early-time underwater explosion (UNDEX) simulations. Dissertation for the Doctoral Degree. Virginia Polytechnic Institute and State University, 2008. 1–130

    Google Scholar 

  18. Barras G, Souli M, Aquelet N, et al. Numerical simulation of underwater explosions using an ALE method. The pulsating bubble phenomena. Ocean Eng, 2012, 41: 53–66

    Google Scholar 

  19. Miller S T, Jasak H, Boger D A, et al. A pressure-based, compressible, two-phase flow finite volume method for underwater explosions. Comput Fluids, 2013, 87: 132–143

    Article  MathSciNet  MATH  Google Scholar 

  20. Hsiao C T, Jayaprakash A, Kapahi A, et al. Modelling of material pitting from cavitation bubble collapse. J Fluid Mech, 2014, 755: 142–175

    Article  MathSciNet  Google Scholar 

  21. Blake J R, Gibson D C. Growth and collapse of a vapour cavity near a free surface. J Fluid Mech, 1981, 111: 123–140

    Article  Google Scholar 

  22. Wang Q X, Yeo K S, Khoo B C, et al. Strong interaction between a buoyancy bubble and a free surface. Theoret Comput Fluid Dyn, 1996, 8: 73–88

    Article  MATH  Google Scholar 

  23. Li S, Zhang A M, Wang S, et al. Transient interaction between a particle and an attached bubble with an application to cavitation in siltladen flow. Phys Fluids, 2018, 30: 082111

    Article  Google Scholar 

  24. Klaseboer E, Khoo B C. Boundary integral equations as applied to an oscillating bubble near a fluid-fluid interface. Comput Mech, 2004, 33: 129–138

    Article  MATH  Google Scholar 

  25. Brujan E A, Keen G S, Vogel A. The final stage of the collapse of a cavitation bubble close to a rigid boundary. Phys Fluids, 2002, 14: 85–103

    Article  MATH  Google Scholar 

  26. Wang Q X, Yeo K S, Khoo B C, et al. Vortex ring modelling of toroidal bubbles. Theor Comput Fluid Dyn, 2005, 19: 303–317

    Article  MATH  Google Scholar 

  27. Li Z R, Sun L, Zong Z, et al. A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface. Acta Mech Sin, 2012, 28: 51–65

    Article  MathSciNet  MATH  Google Scholar 

  28. Li Z, Sun L, Zong Z. Numerical analysis of gas bubbles in close proximity to a movable or deformable body. Arch Appl Mech, 2013, 83: 1715–1737

    Article  MATH  Google Scholar 

  29. Liu Y, Zhang A, Tian Z. Approximation of underwater explosion bubble by singularities based on BEM. Ocean Eng, 2014, 75: 46–52

    Article  Google Scholar 

  30. Zhang A M, Liu Y L. Improved three-dimensional bubble dynamics model based on boundary element method. J Comput Phys, 2015, 294: 208–223

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhang A M, Wu W B, Liu Y L, et al. Nonlinear interaction between underwater explosion bubble and structure based on fully coupled model. Phys Fluids, 2017, 29: 082111

    Article  Google Scholar 

  32. Liu N N, Cui P, Ren S F, et al. Study on the interactions between two identical oscillation bubbles and a free surface in a tank. Phys Fluids, 2017, 29: 052104

    Article  Google Scholar 

  33. Liu G R, Liu M B. Smoothed Particle Hydrodynamics–A Meshfree Particle Method. Singapore: World Scientific Publishing Co. Pte. Ltd, 2003. 1–472

    Google Scholar 

  34. Liu M B, Liu G R. Smoothed particle hydrodynamics (SPH): An overview and recent developments. Arch Computat Methods Eng, 2010, 17: 25–76

    Article  MathSciNet  MATH  Google Scholar 

  35. Hu X Y, Adams N A. An incompressible multi-phase SPH method. J Comput Phys, 2007, 227: 264–278

    Article  MATH  Google Scholar 

  36. Grenier N, Antuono M, Colagrossi A, et al. An Hamiltonian interface SPH formulation for multi-fluid and free surface flows. J Comput Phys, 2009, 228: 8380–8393

    Article  MathSciNet  MATH  Google Scholar 

  37. Monaghan J J, Rafiee A. A simple SPH algorithm for multi-fluid flow with high density ratios. Int J Numer Meth Fluids, 2013, 71: 537–561

    Article  MathSciNet  Google Scholar 

  38. Chen Z, Zong Z, Liu M B, et al. An SPH model for multiphase flows with complex interfaces and large density differences. J Comput Phys, 2015, 283: 169–188

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang Z, Sun L, Yao X, et al. Smoothed particle hydrodynamics simulation of the submarine structure subjected to a contact underwater explosion. Combust Explos Shock Waves, 2015, 51: 502–510

    Article  Google Scholar 

  40. Swegle J W, Attaway S W. On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations. Comput Mech, 1995, 17: 151–168

    Article  MATH  Google Scholar 

  41. Zhang Z, Wang L, Ming F, et al. Application of smoothed particle hydrodynamics in analysis of shaped-charge jet penetration caused by underwater explosion. Ocean Eng, 2017, 145: 177–187

    Article  Google Scholar 

  42. Cao X Y, Ming F R, Zhang A M, et al. Multi-phase SPH modeling of air effect on the dynamic flooding of a damaged cabin. Comput Fluids, 2018, 163: 7–19

    Article  MathSciNet  MATH  Google Scholar 

  43. Wang P, Zhang A M, Ming F, et al. A novel non-reflecting boundary condition for fluid dynamics solved by smoothed particle hydrodynamics. J Fluid Mech, 2019, 860: 81–114

    Article  MathSciNet  MATH  Google Scholar 

  44. Dobratz B M, Crawford P C. LLNL Explosive Handbook: Properties of Chemical Explosives and Explosives and Explosive Simulants. LLNL Report UCRL-52997. 1981

    Google Scholar 

  45. Steinberg D J. Spherical Explosions and the Equation of State of Water. LLNL Technical Report UCID-20974. 1987

    Google Scholar 

  46. Adami S, Hu X Y, Adams N A. A generalized wall boundary condition for smoothed particle hydrodynamics. J Comput Phys, 2012, 231: 7057–7075

    Article  MathSciNet  Google Scholar 

  47. Monaghan J J. Simulating free surface flows with SPH. J Comput Phys, 1994, 110: 399–406

    Article  MATH  Google Scholar 

  48. Zhang Y L, Yeo K S, Khoo B C, et al. 3D jet impact and toroidal bubbles. J Comput Phys, 2001, 166: 336–360

    Article  MATH  Google Scholar 

  49. Cole R H. Underwater Explosion. New Jersey: Princeton University Press, 1948. 118–127

    Google Scholar 

  50. Wang C, Khoo B C. An indirect boundary element method for three-dimensional explosion bubbles. J Comput Phys, 2004, 194: 451–480

    Article  MATH  Google Scholar 

  51. Wu G X, Hu Z Z. Simulation of nonlinear interactions between waves and floating bodies through a finite-element-based numerical tank. Proc R Soc London Ser A-Math Phys Eng Sci, 2004, 460: 2797–2817

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    ZhiFan Zhang & Cheng Wang

  2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, China

    A-Man Zhang

  3. Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough University, Leicestershire, LE11 3TU, UK

    Vadim V Silberschmidt

  4. China Ship Research and Development Academy, Beijing, 100101, China

    LongKan Wang

Authors
  1. ZhiFan Zhang
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  2. Cheng Wang
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  3. A-Man Zhang
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  4. Vadim V Silberschmidt
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  5. LongKan Wang
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Correspondence to ZhiFan Zhang.

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Zhang, Z., Wang, C., Zhang, AM. et al. SPH-BEM simulation of underwater explosion and bubble dynamics near rigid wall. Sci. China Technol. Sci. 62, 1082–1093 (2019). https://doi.org/10.1007/s11431-018-9420-2

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  • DOI: https://doi.org/10.1007/s11431-018-9420-2

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