Abstract The trajectory of the virtual mass centers of sequentially departing gas bubbles in water flow has been analyzed in this study. The bubbles were generated from a brass nozzle of 1 mm inner diameter in a glass tank (300 × 150 × 500 mm3), filled with distilled water maintained at 21 ± 1 °C. A three-mirror system was used to obtain two frames of the workspace in a single shot of a Phantom v1610 high-speed camera. A three-dimensional computer reconstruction algorithm was developed, which consisted of a blur filter, canny edge filter, region of interest (ROI), and Kalman filter. This algorithm was used to obtain the coordinates of the center of mass of each individual gas bubble. We analyzed the bubble trajectories obtained for three different air volumetric flow rates. A multifractal analysis was used to evaluate the gas bubble dynamics. The wavelet transform modulus maxima method was used to obtain the singularity spectra of the bubble paths. The local Holder exponent value proved that the gas bubble motion trajectories tended to behave in a deterministic and chaotic manner. In addition, the sensitivity of the chaotic bubble paths to small- and large-scale fluctuations of the lateral bubble displacement was investigated. In conclusion, the proposed approach allows us to distinguish between deterministic chaotic dynamics and the stochastic evolution of bubble paths.

中文翻译：

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使用图像分析测量气泡路径的多重分形特征

摘要 本研究分析了水流中逐次离开气泡的虚拟质心轨迹。气泡由内径为 1 mm 的黄铜喷嘴在玻璃罐 (300 × 150 × 500 mm3) 中产生，并装有保持在 21 ± 1 °C 的蒸馏水。三镜系统用于在 Phantom v1610 高速相机的单次拍摄中获取工作区的两帧。开发了一种三维计算机重建算法，它由模糊滤波器、canny 边缘滤波器、感兴趣区域 (ROI) 和卡尔曼滤波器组成。该算法用于获得每个单独气泡的质心坐标。我们分析了三种不同空气体积流量下获得的气泡轨迹。使用多重分形分析来评估气泡动力学。采用小波变换模极大值法得到气泡路径的奇异谱。局部 Holder 指数值证明气泡运动轨迹倾向于以确定性和混沌方式表现。此外，研究了混沌气泡路径对横向气泡位移的小尺度和大尺度波动的敏感性。总之，所提出的方法使我们能够区分确定性混沌动力学和气泡路径的随机演化。研究了混沌气泡路径对横向气泡位移的小尺度和大尺度波动的敏感性。总之，所提出的方法使我们能够区分确定性混沌动力学和气泡路径的随机演化。研究了混沌气泡路径对横向气泡位移的小尺度和大尺度波动的敏感性。总之，所提出的方法使我们能够区分确定性混沌动力学和气泡路径的随机演化。