Numerical analysis of air entrainment and flows around a surface-piercing finite circular cylinder

Flows past a surface-piercing finite circular cylinder at various Froude numbers Fr ranging from 0.8 to 1.7 are investigated by utilizing high-fidelity numerical simulation based on the adaptive mesh refinement technique, the geometric volume-of-fluid method, and the embedded boundary method. The primary objective of the study is to reveal the relationship and interactions between the flow field and the air entrainment mechanism in a surface-piercing cylinder flow. Numerical approaches are validated in various aspects by comparing simulation results to previous experimental and numerical data. The detailed flow characteristics, including free surface deformation, velocity fields, and vortex structures at different Froude numbers, are discussed thoroughly. The free surface breaking is captured and characterized by the local surface slope |∇η|, with three distinct breaking regions and two different breaking types identified. Features of the velocity field at various Froude numbers are discovered by analyzing the velocity distributions at certain locations, turbulent kinetic energy, and vortex structures. Bubble statistics including bubble size distribution and spatial distribution are obtained. Three distinct slopes of bubble size distribution Nr∼r−3/2,r−10/3,r−5 are identified for different bubble radius intervals. The bubble spatial distribution is closely related to the Froude number, with the vertical depth of the bubble clouds increasing from y/D=−1.56 at Fr=1.1 to y/D=−2.59 at Fr=1.7. Many distinct flow characteristics are associated with bubble size and spatial distribution, which can be utilized to interpret air entrainment mechanisms and bubble statistics. Moreover, the effects of surface tension on bubble statistics are examined.