Modelling of the free surface deformation and air entrainment behavior in 2D turbulent flows

The dynamic free-surface evolution leading to air entrainment is important for understanding two-phase flow generation. It is, therefore, essential to clarify the inherent response of the microscopic kinetic properties of turbulent surfaces. In the present study, the two dimensional (2D) velocity fields, and shape size scales of a deformed surface in open channel flows are quantitatively described, based on laboratory free surface observations, using particle image velocimetry (PIV) and a high-speed image acquisition system. A surface model, which demonstrates that free-surface spatial correlation patterns could be described as an inverted cone cavity development process, is proposed. The evolution of the entire surface was controlled by multiple mechanical equilibria, above which the surface cavity could not retain the inverted cone shape. Between entrapment cavity collapse and closure generation, bubble entrainment was determined by the surface size scale and kinematic properties of the streamwise shrinking surface. Surface instability and closure conditions were established based on surface dynamics. In addition, series of relationships between surface dynamics and flow conditions were obtained from measurement data. This demonstrates that the observed complex free surface can be modeled as an ensemble of spatial and temporal motion based on free surface interaction mechanics.