Dynamical Equations of Aspherical Bubbles Based on Lagrangian Formalism

• Project/Area Number: 23760142
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Fluid engineering
• Research Institution: Oita University
• Principal Investigator: KURIHARA eru 大分大学, 工学部, 准教授 (90344481)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 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

Research Abstract

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.

Research Products

• [Journal Article] Numerical simulation of nonlinear resonant oscillations in an elliptical cylinder (2012)
  • Author(s): E. Kurihara
  • Journal Title: Proc. ISNA Volume: 19 Pages: 151-154
• [Journal Article] Nonlinear interaction among oscillating non-spherical bubbles (2012)
  • Author(s): E. Kurihara
  • Journal Title: Proc. 19th ISNA Volume: 1474 Pages: 151-154
  • DOI: 10.1063/1.4749318
  • Peer Reviewed
• [Journal Article] Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations (2011)
  • Author(s): E. Kurihara, T. A. Hay, Yu. A. Ilinskii, E. A. Zabolotskaya, M. F. Hamilton
  • Journal Title: J. Acoust. Soc. Am. Volume: 130 Pages: 3357-3369
• [Journal Article] Three-dimensional dynamical equations of (2011)
  • Author(s): E. Kurihara
  • Journal Title: J. Acoust. Soc. Am. Volume: 130 Pages: 2503-2503
  • Peer Reviewed
• [Journal Article] Model for the dynamics of two interacting (2011)
  • Author(s): E. Kurihara et al.
  • Journal Title: J. Acoust. Soc. Am. Volume: 130 Pages: 3357-3369
  • Peer Reviewed
• [Presentation] Nonlinear interaction among oscillating non-spherical bubbles (2012)
  • Author(s): E. Kurihara
  • Organizer: 19th ISNA
  • Place of Presentation: Tokyo, Japan
• [Presentation] 相互作用を考慮した非球形気泡群の非線形振動解析 (2011)
  • Author(s): 栗原央流
  • Organizer: 京都大学数理解析研究所講究録
• [Presentation] 数理的な手法による非球形気泡群の力学挙動解析 (2011)
  • Author(s): 栗原央流
  • Organizer: 第12回九州地区流体工学研究会
• [Presentation] Three-dimensional dynamical equations of interacting bubbles (2011)
  • Author(s): E. Kurihara
  • Organizer: J. Acoust. Soc. Am.
• [Presentation] 多重極展開による気泡の変形と気泡間相互作用の定式化 (2011)
  • Author(s): 栗原央流
  • Organizer: 流体力学会年会2011
  • Place of Presentation: 東京
• [Presentation] 相互作用を考慮した非球形気泡群の非線形振動解析 (2011)
  • Author(s): 栗原央流
  • Organizer: 非線形波動現象の研究の新たな進展（京都大学数理解析研究所研究集会）
  • Place of Presentation: 京都