Numerical study of turbulent two - phase Couette flow

The motivation underpinning this work is the need to understand bubble generation mechanisms due to interactions between free surface and turbulent boundary layers as commonly seen near ship walls. As a canonical problem, we consider a turbulent plane Couette flow with vertical parallel sidewalls and an air-water interface established by gravity in the vertical direction. Two-phase Couette flow has been described in the literature in different flow setups. Most studies were limited to cases of low Reynolds number and the evolution of a single bubble/droplet. Deformation and breakup of a single droplet in a plane Couette flow at low Reynolds number has been studied experimentally, theoretically, and numerically (see e.g., Li et al. 2000; Renardy et al. 2002; Rallison 1984). In another example of the two-phase Couette flow is the two-layers of immiscible fluids which are set between moving horizontal walls. Due to viscosity difference between fluids, there is a jump in the tangential velocity gradient across the interface which induces instabilities at the fluid interface (Coward et al. 1997; Charru & Hinch 2000). At high Reynolds number, there are only a few studies of two-phase Couette flow. Iwasaki et al. (2001) studied the dynamics of a single immiscible drop in turbulent gas flow between two moving walls. Fulgosi et al. (2003); Liu et al. (2009) performed direct numerical simulation (DNS) of interface evolution in Couette flow between two moving horizontal walls. One interesting case of a two-phase Couette flow in a turbulent regime is when the initial interface is set to be orthogonal to the moving vertical walls. In such a setup, the interaction between the fluid interface and the turbulent boundary layer is a key phenomenon. At sufficiently high Reynolds, Weber and Froude numbers, shearinduced interfacial waves can break, which leads to the formation of air cavities. These air cavities will be further fragmented by turbulence to smaller bubbles. These complexities make two-phase Couette flow at high Reynolds number a challenging problem for both experiments and numerical analysis. Capturing the small-scale flow and interface features requires high-resolution experimental techniques and very expensive DNS calculations. Only two numerical studies (Kim et al. 2012, 2013) have been performed for investigation of air entrainment and bubble generation in two-phase Couette flow. The current work is a continuation of our recent studies (Kim et al. 2012, 2013), where we performed numerical simulations of the interface breakup in two-phase Couette flow at Reynolds number of approximately 13000 and Weber number of approximately 42000 (surface tension coefficient was much smaller than the realistic value for an air-water system). The effect of Froude number on the interface breakup and bubble generation was studied in Kim et al. (2012). The second paper of Kim et al. (2013) was mostly devoted to the development and assessment of a mass conservative interface-capturing method based on a geometric volume-of-fluid (VOF) approach, and one simulation of