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中文摘要：
在应用边界元方法对气泡动力学的研究中,绝大多数模型是建立在不压缩势流理论基础之上,针对可压缩流场中气泡运动特性的研究很少.从波动方程出发,分别在气泡运动前期和后期对波动方程进行简化,得到气泡运动局部和全局简化方程,采用双渐进方法对简化方程进行匹配,提出了考虑流场可压缩性的非球状气泡运动模型.该模型的计算结果与Prospertti等的解析结果吻合很好,气泡脉动最大半径和内部最大压力随气泡脉动逐渐减小.基于该模型对比了自由场中药包爆炸考虑可压缩性与不考虑可压缩性的计算结果,发现考虑可压缩性气泡射流速度较小,随后基于该模型计算了刚性边界下气泡的运动特性.
英文摘要：
Most studies on bubble dynamics adopting the boundary element method （BEM） were based on the incompressible potential flow theory, and the motion and deformation of a bubble in a compressible liqhid was rarely studied by using BEM. An approximate theory is developed for a nonlinear and non-spherical bubble in a compressible fluid by using the doubly asymptotic approximation method. Wave equation is approximated in the early and late stages, respectively, resulting in the so-called local and global approximation equations. Matching between these two equations provides the model for the non-spherical bubble behavior in a compressible fluid domain. The numerical model is validated against the Prospertti ＆ Lezzi equation for spherical bubbles in weakly compressible liquids with excellent agreement being obtained for the bubble radius evolution up to the second oscillation. Both numerical result and theoretical analysis show that the maximum radius decreases as the bubble oscillates. Numerical analyses are further performed for non-spherical oscillating bubbles. Bubble evolution and jet formation are simulated. Compared with that of the incompressible model, the jet velocity in the present model is smaller. Bubble oscillation near a solid boundary is further simulated based on the present model.
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