SPH-BEM simulation of underwater explosion and bubble dynamics near rigid wall
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摘要
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.
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.
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.
引文
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
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
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
4 Cui P, Zhang A M, Wang S P, et al. Ice breaking by a collapsing bubble. J Fluid Mech, 2018, 841:287–309
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
6 Snay H G. Underwater Explosion Phenomena:The Parameters of Migrating Bubbles. NAVORD Report. 1962
7 Snay H G, Tipton R V. Charts for the Parameters of Migrating Explosion Bubbles. NAVORD Report. 1962
8 Klaseboer E, Hung K C, Wang C, et al. Experimental and numerical investigation of the dynamics of an underwater explosion bubble neara resilient/rigid structure. J Fluid Mech, 2005, 537:387–413
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
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
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
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
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
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
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
16 Cui P, Zhang A M, Wang S P. Small-charge underwater explosion bubble experiments under various boundary conditions. Phys Fluids,2016, 28:117103
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
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
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
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
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
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
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
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
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
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
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
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
29 Liu Y, Zhang A, Tian Z. Approximation of underwater explosion bubble by singularities based on BEM. Ocean Eng, 2014, 75:46–52
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
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
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
33 Liu G R, Liu M B. Smoothed Particle Hydrodynamics–A Meshfree Particle Method. Singapore:World Scientific Publishing Co. Pte. Ltd,2003. 1–472
34 Liu M B, Liu G R. Smoothed particle hydrodynamics(SPH):An overview and recent developments. Arch Computat Methods Eng,2010, 17:25–76
35 Hu X Y, Adams N A. An incompressible multi-phase SPH method. J Comput Phys, 2007, 227:264–278
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
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
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
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
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
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
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
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
44 Dobratz B M, Crawford P C. LLNL Explosive Handbook:Properties of Chemical Explosives and Explosives and Explosive Simulants.LLNL Report UCRL-52997. 1981
45 Steinberg D J. Spherical Explosions and the Equation of State of Water. LLNL Technical Report UCID-20974. 1987
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
47 Monaghan J J. Simulating free surface flows with SPH. J Comput Phys, 1994, 110:399–406
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
49 Cole R H. Underwater Explosion. New Jersey:Princeton University Press, 1948. 118–127
50 Wang C, Khoo B C. An indirect boundary element method for three-dimensional explosion bubbles. J Comput Phys, 2004, 194:451–480
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
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
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
4 Cui P, Zhang A M, Wang S P, et al. Ice breaking by a collapsing bubble. J Fluid Mech, 2018, 841:287–309
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
6 Snay H G. Underwater Explosion Phenomena:The Parameters of Migrating Bubbles. NAVORD Report. 1962
7 Snay H G, Tipton R V. Charts for the Parameters of Migrating Explosion Bubbles. NAVORD Report. 1962
8 Klaseboer E, Hung K C, Wang C, et al. Experimental and numerical investigation of the dynamics of an underwater explosion bubble neara resilient/rigid structure. J Fluid Mech, 2005, 537:387–413
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
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
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
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
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
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
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
16 Cui P, Zhang A M, Wang S P. Small-charge underwater explosion bubble experiments under various boundary conditions. Phys Fluids,2016, 28:117103
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
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
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
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
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
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
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
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
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
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
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
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
29 Liu Y, Zhang A, Tian Z. Approximation of underwater explosion bubble by singularities based on BEM. Ocean Eng, 2014, 75:46–52
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
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
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
33 Liu G R, Liu M B. Smoothed Particle Hydrodynamics–A Meshfree Particle Method. Singapore:World Scientific Publishing Co. Pte. Ltd,2003. 1–472
34 Liu M B, Liu G R. Smoothed particle hydrodynamics(SPH):An overview and recent developments. Arch Computat Methods Eng,2010, 17:25–76
35 Hu X Y, Adams N A. An incompressible multi-phase SPH method. J Comput Phys, 2007, 227:264–278
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
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
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
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
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
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
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
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
44 Dobratz B M, Crawford P C. LLNL Explosive Handbook:Properties of Chemical Explosives and Explosives and Explosive Simulants.LLNL Report UCRL-52997. 1981
45 Steinberg D J. Spherical Explosions and the Equation of State of Water. LLNL Technical Report UCID-20974. 1987
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
47 Monaghan J J. Simulating free surface flows with SPH. J Comput Phys, 1994, 110:399–406
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
49 Cole R H. Underwater Explosion. New Jersey:Princeton University Press, 1948. 118–127
50 Wang C, Khoo B C. An indirect boundary element method for three-dimensional explosion bubbles. J Comput Phys, 2004, 194:451–480
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