空泡动力学中过阻尼系统的存在性分析

EXISTENCE ANALYSIS OF OVER DAMPED SYSTEM IN BUBBLE DYNAMICS

  • 摘要: 在空泡动力学研究中,阻尼机制对气泡泡壁运动具有非常重要的影响。空泡动力学中所涉及的阻尼机制一般分为3种:黏性阻尼、热阻尼、声阻尼。本文基于泡壁运动方程,通过理论分析和推导,从主导阻尼机制的角度对气泡半径进行了分区讨论,获得了简化的阻尼比公式,证明了空泡动力学中过阻尼系统的存在性。与亚阻尼系统相比,过阻尼系统中的气泡并非进行衰减的往复简谐振荡,而是从初始位置逐步衰减至平衡位置。

     

    Abstract: Damping mechanisms play a crucial role in the dynamics of bubble, significantly impacting the motion of the bubble wall. The damping mechanisms can be classified into three types: viscous damping, thermal damping, and acoustic damping. This paper provides an in-depth study of the dynamics of the bubble wall through a detailed analysis of the dominant damping mechanisms governing their behavior and delineating the range of bubble radii. Through theoretical analysis and derivation of the equations governing bubble wall motion, the simplified damping ratio equation is established. This equation serves as evidence for the existence of an over-damped system in bubble dynamics. In contrast to the sub-damped system, where the bubble undergoes decaying reciprocal simple harmonic oscillations, the bubble in the over-damped system exhibits a distinct behavior. Rather than oscillating, the bubble gradually decays from its initial position towards its equilibrium position. This observation sheds light on the distinct behavior exhibited by bubble under different damping systems.

     

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