As a conventional and persistent topic, a single bubble freely ascending in Newtonian liquids is investigated based on its shape and motion predictions using the strategy of machine learning. The dataset for training, validating, and testing neural networks is composed of the current experimental results and the extensively collected data from previous research works, which covers a broad range of dimensionless parameters that are [Formula: see text], and [Formula: see text]. The novel models of the aspect ratio E and drag coefficient [Formula: see text] are proposed based on a backpropagation neural network. The comparisons of the conventional correlations indicate that the new E model presents a significant superiority. This E model also has a good capability to predict the minimum E as about 0.26 that is consistent with the theoretical value [Formula: see text]. Moreover, the [Formula: see text] models are divided into E-independent and E-dependent types. The performances of these two type models are quite similar and both agree well with the experimental results. The errors of the [Formula: see text] predictions for Re > 1 are mostly in the range of [Formula: see text].
For decades, it has been proven by numerous experiments and simulations that a single bubble freely rises in an unstable path and shape in a surface tension force dominant regime. Using time-resolved tomographic particle image velocimetry combined with three-dimensional shadow image reconstruction, the present study experimentally provides a full three-dimensional diagnosis of the shape and wake structures of a zigzagging bubble. An ellipsoidal bubble with an equivalent diameter of [Formula: see text] = 5.47 mm freely rising in stagnant water is investigated at a terminal Reynolds number of 1390 with a zigzag path. The results show a typical double-threaded vortex structure generated during the initial ascending stage. In the regular zigzagging stage, a four-ring mode of vortex generation is observed, which is composed of alternatively discharged and induced hairpin vortices. Thanks to the volumetric measurement, the shedding or inducing mechanism of complicated wake structures is clearly achieved. We speculate that the secondary shape oscillation of the bubble is excited by the shedding of the primary hairpin vortex. Frequencies of the bubble trajectory, variation of velocity, and bubble shape oscillation are analyzed in detail. Their associated harmonics are classified to indicate the interactions between the bubble and the wakes.
Volumetric measurement for the non-cavitating tip vortex in the near field of an elliptical hydrofoil is conducted using tomographic particle image velocimetry (TPIV), which provides a fully three-dimensional diagnose of the vortex formation and development. The wandering motion and flow properties of the near-field tip vortex under different incident angles and Reynolds numbers are investigated in detail. Unlike in the far field, the wandering motion in the near field is mainly subject to the local flow unsteadiness rather than the flow condition. By the "re-centered" post-processing, the deviations introduced by the wandering motion can be technically corrected, and more accurate vortex properties can be thus obtained. In the near field, a turning point of the vortex center trajectory is detected, the position of which is basically independent of the flow condition. By investigating the local flow properties, it is found that this turning point is the position where the tip vortex completely leaves the trailing edge of hydrofoil and enters the wake region. At this turning point, the external supply to the vortex core starts to be restricted, and the vortex circulation reaches a rather constant value. Further according to the local flow properties, the development process of the near-field tip vortex can be divided into three stages: vortex-attached stage, vortex-lifting stage and vortex-detached stage, which are found to be closely relevant to the hydrofoil configuration.
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