The interaction of two underwater explosion bubbles was mathematically analyzed in this paper. Based on the assumption of potential flow, high-order curved elements were used to discretize the boundary integral equati...The interaction of two underwater explosion bubbles was mathematically analyzed in this paper. Based on the assumption of potential flow, high-order curved elements were used to discretize the boundary integral equation and solve it. Assuming that gas inside the bubble follows the isentropic rule, the Euler-Lagrange method was used to trace the evolution of the bubble, and when calculating the singular integral, the singularity of the double-layer singular integral was eliminated by reconstructing a principal-value integral of double-layer potential so that a more precise result could be obtained. Elastic mesh technique (EMT) was also used when tracing the evolution of the bubble interface, and numerical smoothing wasn't needed. A comparison of calculations using this three-dimensional model with results of the Reyleigh-Plesset bubble model shows that the three-dimensional model and calculation method in this paper is practical. This three-dimensional model was applied to simulate the interaction of two bubbles under the action of gravity, and the dynamic characteristics of two bubbles near the surface was also analyzed. Bubbles influenced by surface effects and gravity present severe non-linearity. This paper provides a reference for research into the dynamics of multi-bubbles.展开更多
文摘The interaction of two underwater explosion bubbles was mathematically analyzed in this paper. Based on the assumption of potential flow, high-order curved elements were used to discretize the boundary integral equation and solve it. Assuming that gas inside the bubble follows the isentropic rule, the Euler-Lagrange method was used to trace the evolution of the bubble, and when calculating the singular integral, the singularity of the double-layer singular integral was eliminated by reconstructing a principal-value integral of double-layer potential so that a more precise result could be obtained. Elastic mesh technique (EMT) was also used when tracing the evolution of the bubble interface, and numerical smoothing wasn't needed. A comparison of calculations using this three-dimensional model with results of the Reyleigh-Plesset bubble model shows that the three-dimensional model and calculation method in this paper is practical. This three-dimensional model was applied to simulate the interaction of two bubbles under the action of gravity, and the dynamic characteristics of two bubbles near the surface was also analyzed. Bubbles influenced by surface effects and gravity present severe non-linearity. This paper provides a reference for research into the dynamics of multi-bubbles.
