水下爆炸气泡的边界积分法及气—液—固相互作用问题的研究
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摘要
近年来,水下爆炸气泡对舰船和海上结构物的破坏受到广泛关注。本文侧重讨论水下爆炸气泡动力学数值计算问题。水下爆炸气泡具有体积变化大、收缩阶段呈非球形、溃灭时产生高速射流等特点。气泡运动过程中涉及到大变形、动边界和多相介质流动问题,给数值计算提出了巨大的挑战。水下爆炸气泡尺度较大、雷诺数较高,因此粘性、可压缩性和表面张力可以忽略,流体运动满足三维不可压缩势流理论。
在不可压缩理论假定下,本文发展了三维可动边界的边界积分法,以模拟气泡非球形生长、溃灭和反弹的动力学过程。气泡初始运动近似满足Rayleigh-Plesset方程。气泡表面采用三角形单元划分,物理空间与参数空间之间的单元满足线性映射关系。气泡表面积分函数采用二维高斯积分求解,大大地提高了计算精度和效率。影响系数阵的奇异性分别通过极坐标变换、去奇异边界积分以及直接求解法等多种方式进行处理,较好地解决了三维边界积分计算中这一难题。在三维数值计算中,射流发展阶段可能出现严重的数值不稳定性,本文采用基于双二次插值多项式的光顺算法使得气泡从单连通到双连通区域的过渡更加光滑稳定。在射流发展过程中单元和节点会过分聚集到射流部分,其他部分的网格和单元变得十分稀疏。采用基于能量最小法则的弹性网格算法,网格演变采用最优速度推进,大大改善了计算中的网格畸变问题。本文通过边界积分算法和涡环模型相结合的方式,成功地模拟了三维模型中射流撞击、穿透以及气泡的反弹过程。计算结果同理论解、实验结果和其他数值结果吻合良好。数值计算的范围包含：气泡在无限流场中的运动、气泡和自由液面的大变形运动、气泡在固定结构周围的演化、气泡与运动刚体、变形薄壳结构的非线性耦合运动。
在气泡与液面大变形运动计算中,基于球面三角形理论,采用直接计算法处理非封闭区域中系数矩阵对角元素的奇异性问题。系统地研究了不同初始位置、浮力参量、初始大小以及底部边界等因素对气泡形状、射流速度和特征参量的影响,分析了液面水冢和气泡内部射流的运动特征。对于多个气泡的研究,详细讨论了气泡之间、气泡与液面间的相互作用、Kelvin冲量以及流场压力的变化特征。
在气泡与固定结构的耦合计算中,详细推导了气泡与结构间的流固耦合算法。基于边界积分基本解的积分恒等式,结合三维内域和外域问题中积分方程的特征关系,采用去奇异积分算法有效地消除了系数矩阵对角线上的弱奇异性问题。本文详细计算了气泡在平板上方、狭长平板间以及柱体附近的演变特征。分析了初始位置、浮力参量、流场压力变化等因素对气泡演化、迁移和射流发展的影响,并详细考察了柱体周围气泡动态变化引起的结构冲击效应。
在气泡与运动刚体研究中,采用浸没球体和圆柱体作为计算模型,通过联立求解边界积分方程和六个自由度的刚体动力学方程,计算了气泡与运动刚体间的三维非线性耦合运动问题。比较了运动刚体和固定刚体对气泡演化和特征参量的影响。在气泡与弹性结构的流固耦合计算中,本文采用细长椭球形壳体模型,将边界积分程序与结构有限元代码结合,详细研究了水面下方近场气泡和弹性壳体的运动特点,为实际的工程应用提供了一定的参考。
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.
在不可压缩理论假定下,本文发展了三维可动边界的边界积分法,以模拟气泡非球形生长、溃灭和反弹的动力学过程。气泡初始运动近似满足Rayleigh-Plesset方程。气泡表面采用三角形单元划分,物理空间与参数空间之间的单元满足线性映射关系。气泡表面积分函数采用二维高斯积分求解,大大地提高了计算精度和效率。影响系数阵的奇异性分别通过极坐标变换、去奇异边界积分以及直接求解法等多种方式进行处理,较好地解决了三维边界积分计算中这一难题。在三维数值计算中,射流发展阶段可能出现严重的数值不稳定性,本文采用基于双二次插值多项式的光顺算法使得气泡从单连通到双连通区域的过渡更加光滑稳定。在射流发展过程中单元和节点会过分聚集到射流部分,其他部分的网格和单元变得十分稀疏。采用基于能量最小法则的弹性网格算法,网格演变采用最优速度推进,大大改善了计算中的网格畸变问题。本文通过边界积分算法和涡环模型相结合的方式,成功地模拟了三维模型中射流撞击、穿透以及气泡的反弹过程。计算结果同理论解、实验结果和其他数值结果吻合良好。数值计算的范围包含：气泡在无限流场中的运动、气泡和自由液面的大变形运动、气泡在固定结构周围的演化、气泡与运动刚体、变形薄壳结构的非线性耦合运动。
在气泡与液面大变形运动计算中,基于球面三角形理论,采用直接计算法处理非封闭区域中系数矩阵对角元素的奇异性问题。系统地研究了不同初始位置、浮力参量、初始大小以及底部边界等因素对气泡形状、射流速度和特征参量的影响,分析了液面水冢和气泡内部射流的运动特征。对于多个气泡的研究,详细讨论了气泡之间、气泡与液面间的相互作用、Kelvin冲量以及流场压力的变化特征。
在气泡与固定结构的耦合计算中,详细推导了气泡与结构间的流固耦合算法。基于边界积分基本解的积分恒等式,结合三维内域和外域问题中积分方程的特征关系,采用去奇异积分算法有效地消除了系数矩阵对角线上的弱奇异性问题。本文详细计算了气泡在平板上方、狭长平板间以及柱体附近的演变特征。分析了初始位置、浮力参量、流场压力变化等因素对气泡演化、迁移和射流发展的影响,并详细考察了柱体周围气泡动态变化引起的结构冲击效应。
在气泡与运动刚体研究中,采用浸没球体和圆柱体作为计算模型,通过联立求解边界积分方程和六个自由度的刚体动力学方程,计算了气泡与运动刚体间的三维非线性耦合运动问题。比较了运动刚体和固定刚体对气泡演化和特征参量的影响。在气泡与弹性结构的流固耦合计算中,本文采用细长椭球形壳体模型,将边界积分程序与结构有限元代码结合,详细研究了水面下方近场气泡和弹性壳体的运动特点,为实际的工程应用提供了一定的参考。
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.
引文
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