丛聚的含气泡水对线性声传播的影响

含气泡水内气泡的空间分布会对线性声传播产生影响,导致实验结论与理论预测存在较大偏差.为解决这一问题,将准晶体近似引入到自洽方法中,导出了考虑空间分布时多分散含气泡水的等效声波波数.考虑到含气泡水内,气泡间存在小范围的聚集趋势(简称丛聚现象),在此基础上引入Neyman-Scott点过程描述了含气泡水内气泡的丛聚现象.分析发现,丛聚时,声速、声衰减的峰值将受到抑制,并向低频偏移,且抑制和频偏现象会随丛聚加剧而变强;随频率远离峰值段,丛聚对声传播的影响逐渐减弱.此外,考虑到空间分布的统计信息提取对相关研究的精确与否起到重要作用,引入了一种比例无偏估计,通过该方法获得了仿真环境下丛聚含气泡水模型的相速度及衰减系数,该建模及统计方法也可为相关实验工作提供理论基础.

Linear-wave propagation in liquids containing bubbly clusters

Acoustic wave propagation in polydisperse bubbly liquids is relevant to diverse applications, such as ship propellers, underwater explosions, and biomedical applications. The simulation of bubbly liquids can date back to Foldy who presented a general theory. In the linear regime, two frequently used models for bubbly liquids are based on the continuum theory and on the multiple scattering theory. Under the homogenization-based assumption, models based on the volume-averaged equations or on the ensemble-averaged equations are designed to find the solutions of a given two-phase flow. The effective wave number is derived through the linearization of these equations. A second approach to the problem of linear wave propagation utilizes the multiple scattering theory. Bubbles are treated as point-like scatterers, and the total field at any location can be predicted by multiple scattering of scatterers. However, in most of experimental researches, the comparison between the approaches and the experimental results is not satisfactory for frequencies near the peak of phase speed and attenuation. In fact, the discrepancies between measurements and approaches are irregular, and the explanations of these discrepancies need further studying. We indicate that such a discrepancy should be attributed to an implicit assumption in these approaches:the bubbles are spatially uniform distribution and statistically independent of each other. In contrast, the complex bubble structures can be observed in many practical bubbly liquids which have important consequences for the acoustic wave propagation. In this paper, our intent is to model the effect of small bubble cluster on linear-wave propagation in bubbly liquids using the self-consistent method. The quasi-crystal approximation is applied to the self-consistent method, and the effective wave number is derived. According to the experimental results, the small clusters of bubbles often exist in bubbly liquids. Therefore, a three-dimensional random model, the Neyman-Scott point process, is proposed to simulate bubbly liquid with the cluster structure. Using this method, we study the influence of such a phenomenon on acoustic dispersion and attenuation relation. A formula for effective wavenumber in clustered bubbly liquid is derived. Compared with the results from the equation of Commander and ProsperettiJ. Acoust. Soc. Am. 85 732 (1989)], our results show that the clustering can suppress peaks in the attenuation and the phase velocity, each of which is a function of frequency. Further, we provide a numerical method. A clustered bubbly liquid is simulated with strict mathematical method and the statistical information is obtained through ratio-unbiased statistical approach. Using such a method, we quantificationally analyze the influence of estimated value on predictions.