Dynamical Equations of Aspherical Bubbles Based on Lagrangian Formalism

基于拉格朗日形式的非球面气泡动力学方程

• 批准号: 23760142
• 负责人: KURIHARA eru
• 金额: $ 1.91万
• 依托单位: Oita University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23760142/
• 关键词: 気泡; 混相流; ラグランジュ力学; 解析力学; キャビテーション; 超音波; 多重曲展開; 衝撃波; 結石破砕

The dynamical equations for interacting non-spherical bubbles are derived theoretically in the framework of Lagrangian formalism with multipole expansion of the bubble boundaries. The bubble boundaries are expanded with spherical harmonics so that deformation and translation of the bubbles can be treated. In order to compose the Lagrangian of the system, corresponding amplitudes of the spherical harmonics are chosen as the generalized coordinate. The derived equations show the observed behaviour such as bubble deformation and onset of jetting. The study mainly takes account of the order of the spherical harmonics up to 3rd mode (octupole mode) because octupole mode is the lowest mode oscillation contributing asymmetrical deformation of the bubble and this has the most significant effect on the behaviour of the bubbles.

在拉格朗日形式的框架下，考虑气泡边界的多极展开，从理论上推导了非球形气泡相互作用的动力学方程。气泡边界用球谐函数展开，从而可以处理气泡的变形和平移。为了构成系统的拉格朗日量，选取相应的球谐函数的幅值作为广义坐标。所导出的方程显示了观察到的气泡变形和喷流开始等行为。由于八极模是导致气泡不对称变形的最低模振荡，对气泡的行为有最大的影响，所以本文主要考虑球谐振级到三阶(八极模)。

项目成果

数理的な手法による非球形気泡群の力学挙動解析

使用数学方法分析非球形气泡的力学行为

• 发表时间: 2011
• 作者: Yuichi MURAI;Ichiro KUMAGAI;Yuji TASAKA;Yoshiaki TAKAHSHI;栗原央流
• 通讯作者: 栗原央流

Numerical simulation of nonlinear resonant oscillations in an elliptical cylinder

椭圆柱体非线性共振的数值模拟

• 发表时间: 2012
• 期刊: Proc. ISNA
• 作者: Joon-wan Kim;Shinichi Yokota;Kazuya Edamura;Hiroki Tomori,Taro Nakamura,;川口雅弘;E. Kurihara
• 通讯作者: E. Kurihara

Three-dimensional dynamical equations of

三维动力学方程

• 发表时间: 2011
• 期刊: J. Acoust. Soc. Am.
• 作者: Hiroki TOMORI;Hiroyuki MAEDA and Taro NAKAMURA;E. Kurihara
• 通讯作者: E. Kurihara

Three-dimensional dynamical equations of interacting bubbles

相互作用气泡的三维动力学方程

• 发表时间: 2011
• 作者: Takumi Watanabe;Dai Tanaka;Daich Kamo;Taro Nakamura;江口 隆夫，古賀 毅，青山 和浩;日比貴之，崔埈豪，加藤孝久，川口雅弘;E. Kurihara
• 通讯作者: E. Kurihara

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

• DOI: 10.1121/1.3626137
• 发表时间: 2011-11-01
• 期刊: JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
• 影响因子: 2.4
• 作者: Kurihara, Eru;Hay, Todd A.;Hamilton, Mark F.
• 通讯作者: Hamilton, Mark F.