Kumar S, Brennen C E
California Institute of Technology, Pasadena 91125.
J Acoust Soc Am. 1991 Feb;89(2):707-14. doi: 10.1121/1.1894630.
This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillation of a single bubble in an infinite fluid. This is used in the approximate solution of the oscillating wall problem, and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. Harmonic generation results from the nonlinearity. It is observed that the bubble natural frequency remains the dominant natural frequency in the volume oscillations of the bubbles near the wall. On the other hand, the pressure perturbations near the wall are dominated by the first and second harmonics present at twice the natural frequency while the pressure perturbation at the natural frequency of the bubble is inhibited. The response at the forcing frequency and its harmonics is explored along with the variation with amplitude of wall oscillation, void fraction, and viscous and surface tension effects. Splitting and cancellation of frequencies of maximum and minimum response due to enhanced nonlinear effects are also observed.
本文对含气泡流体对垂直于自身振动的壁面运动的响应进行了频谱分析。首先，对瑞利 - 普莱斯方程进行傅里叶分析，以获得无限流体中单个气泡振荡时非线性效应的近似解。这被用于振荡壁面问题的近似解中，并对所得表达式进行数值评估，以研究非线性效应。谐波的产生源于非线性。可以观察到，气泡固有频率在靠近壁面的气泡体积振荡中仍然是主导固有频率。另一方面，壁面附近的压力扰动由两倍固有频率处的一次和二次谐波主导，而气泡固有频率处的压力扰动受到抑制。研究了强迫频率及其谐波处的响应以及壁面振荡幅度、空隙率、粘性和表面张力效应的变化。还观察到由于增强的非线性效应导致的最大和最小响应频率的分裂和抵消。
