A Study Of Underwater Explosion Bubbles And Gas-Liquid-Solid Interaction Problems Using Boundary Integral Method

In recent years, the dynamics of underwater explosion bubble has attracted extensive attentions among researchers due to its seriously damaging effects on warships and marine structures. In the present study, more focus is cast on the investigation into dynamical characteristics of underwater explosion bubbles near complex boundaries such as free surfaces, moving or deformable boundaries. The underwater explosion bubble is characterized by the large volume variation, non-spherical collapse and the formation of high-speed liquid jet. The bubble evolution is accompanied by complex physical properties such as large deformations, moving boundaries and multi-phase flows, which pose great challenges to many numerical methodologies. Due to large dimensions and high Reynolds number of underwater explosion bubble, the fluid can be assumed to be inviscid, incompressible, and the flow irrotational.Based upon this simplification, a potential-flow boundary integral method is developed to simulate the growth and collapse of non-spherical bubbles undergoing large contortions and deformations near complex boundaries. The bubble motion in the initial phase can be approximately described by the Rayleigh-Plesset equation. The bubble surface is divided into many triangular elements, and the mapping of elements in physical space onto parametric space is assumed to be linear. Surface integral functions are calculated by two-dimensional Gaussian quadrature formulae for triangle. The singularities of the influence coefficients are eliminated via several different methods such as the polar coordinate transformation, desingularizing formulation and direct calculation approach. The formation of liquid jet and the ensuing jet impact during collapse may lead to strong numerical instabilities. A new smoothing scheme based on least squares is adopted to dampen the strong instabilities of the jetting process, enabling a smooth transition from a singly connected bubble to a doubly connected one. For asymmetric bubble deformation, the elements and nodes are attracted to the jet tip vicinity, which has the consequence of thinning out the element distribution in other regions. The elastic mesh technique based on the principle of minimum elastic potential energy is adopted. The mesh nodes is advected by the optimum shift velocity to make the element distribution as reasonably uniform as possible and enable the computation more stable and robust. The combination of the boundary integral method and a vortex ring model is used to simulate the process of jet impact, penetration and the toroidal bubble rebound. Our calculation results are in satisfactory agreements with the theoretical solution, experimental results as well as other numerical results. Numerical simulations in the paper include:the bubble growth and collapse in an infinite fluid, the large deformation between the bubbles and free surface, and the nonlinear fluid-structure interaction between bubble and fixed structure as well as the nonlinear coupled response of moving or deformable structures to bubble dynamics.For large deformations of between the free surface and bubbles, the singularities of influence coefficients for the open surface are cancelled by using a direct calculation of spatial angles. The influences of the initial positions, buoyancy parameters, initial sizes and bottom boundary on the evolution of bubble shapes near a free surface are investigated. The dynamical characteristics of the free surface spike and bubble jetting are analyzed. For interactions of multiple bubbles, the evolution of shapes, the variation of Kelvin impulse and the pressure distributions in the flow field between bubbles and the free surface are examined comprehensively.For the problems of bubble motions near fixed structures, the fluid-structure interaction algorithm between bubble and fixed structures is deduced in detailed and the desingularized boundary element formulation for eliminating the weakly-singular terms of influence coefficient matrices are presented. The evolution of bubbles in proximity to a square plate, two parallelled plates and curved walls are investigated. The bubble shapes, jetting patterns and bubble migrations under different initial positions, buoyancy parameters and pressure distributions are obtained. The characteristics of dynamic loading induced by bubble evolution on the cylinder are discussed in detail.The growth and collapse of gaseous bubbles near a movable or deformable body are presented numerically using the boundary integral method and fluid-structure interaction technique. Using a submerged sphere and cylinder as calculation models, the six-degrees-of-freedom equations of motion for the rigid body are solved interactively in conjunction with the boundary integral equation. The characteristics of nonlinear motions between bubble and movable structure are analyzed. The motion of bubbles near a deformable structure is also simulated using the combination of boundary integral method (BIM) and finite element method (FEM). The growth and collapse of bubbles near a deformable ellipsoid shell in the presence of the free surface are investigated, and the dynamical characteristics during the bubble motions have been summarized.