Tip vortex cavitation (TVC) is an important type of cavitation. There is an urgent need for the accurate prediction of its inception condition. The water quality, i.e., the distribution of nuclei, is one of the main contributors to the TVC inception. Since there is no available cavitation model involving the effect of water quality, a new model suitable for TVC prediction is investigated based on the bubble dynamics. The migration and growth of nuclei are simulated in a tip vortex flow. An analytic method is developed to calculate the capture time of nuclei so that we can determine the critical nucleus in a vortex flow according to a filtering principle. The comparisons of the effect of water quality obtained in simulations and analytics are performed. It validates that the embodiment of water quality is rational and the analytical method is applicable for engineering purpose. Finally, the prediction model is quantitatively improved by considering the effect of water quality, and it is a new model for the prediction of tip vortex cavitation inception.

This paper investigates numerically the collapses of both a single cavitation bubble and a cluster consisting of 8 bubbles, concerning mainly on the conversions between different forms of energy. Direct numerical simulation (DNS) with volume of fluid (VOF) method is applied, considering the detailed resolution of the vapor-liquid interfaces. First, for a single bubble near a solid wall, we find that the peak value of the wave energy, or equivalently the energy conversion rate decreases when the distance between the bubble and the wall is reduced. However, for the collapses of multiple bubbles, this relationship between the bubble-wall distance and the conversion rate reverses, implying a distinct physical mechanism. The evolutions of individual bubbles during the collapses of multiple bubbles are examined. We observe that when the bubbles are placed far away from the solid wall, the jetting flows induced by all bubbles point towards the cluster centre, while the focal point shifts towards the solid wall when the cluster is very close to the wall. We note that it is very challenging to consider thermal and acoustic damping mechanisms in the current numerical methods, which might be significant contributions to the energy budget, and we leave it open to the future studies.

The unsteady cavitation typically includes three processes: the growth of cavitation, the instability and shedding of cavitation, and the collapse of cloud cavitation and the regeneration of attached cavitation. In this paper, the unsteady features of the cavitating flow past a sphere are investigated. A detached eddy simulation turbulence model and a transport equation cavitation model are used to model the cavitating flow. The numerical results give the unsteady process of cavitation at different cavitation numbers (0.36 < σ < 1.0), which cover the cavitation state from inception to supercavitation. When the cavitation number 0.8 < σ < 1.0, the flow instability belongs to the single frequency mode; when the cavitation number σ < 0.8, the flow instability becomes the dual-frequency mode. We analyzed the Strouhal (St) number based on the length of the cavitation and found that the St numbers are stable around 0.5 and 0.2 in the dual-frequency mode. In this mode, the high frequency corresponds to the frequency of the large-scale cavity shedding caused by repeated re-entrant jets. The low frequency, caused by the combination of wake flow and cavitation, is close to the natural frequency of the sphere. In addition, the cavity leading edge position and cavity morphology are analyzed in details. Some of the numerical results are compared with existing experimental data.

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 $d_{eq}$ = 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.

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 ${10}^{-3}\le Re\le {10}^5,\hspace{0.17em}{10}^{-2}\le Eo\le {10}^3,\hspace{0.17em}{10}^{-5}\le We\le {10}^2$ , and ${10}^{-14}\le Mo\le {10}^7$ . The novel models of the aspect ratio E and drag coefficient $C_D$ 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 $E_{We\to \infty }\approx 0.25$ . Moreover, the $C_D$ 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 $C_D$ predictions for Re > 1 are mostly in the range of $\pm 20\%$ .