Air Entrainment and Surface Fluctuations in a Turbulent Ship Hull Boundary Layer

Abstract

The air entrainment due to the turbulence in a free surface boundary layer shear flow created by a horizontally moving vertical surface-piercing wall is studied through experiments and direct numerical simulations.In the experiments, a laboratory-scale device was built that utilizes a surface-piercing stainless steel belt that travels in a loop around two vertical rollers, with one length of the belt between the rollers acting as a horizontally-moving flat wall. The belt is accelerated suddenly from rest until reaching constant speed in order to create a temporally-evolving boundary layer analogous to the spatially-evolving boundary layer that would exist along a surface-piercing towed flat plate. To complement the experiments, Direct Numerical Simulations (DNS) of the two-phase boundary layer problem were carried out with the domain including a streamwise belt section simulated with periodic boundary conditions. Cinematic Laser-Induced Fluorescence (LIF) measurements of water surface profiles in two vertical planes oriented parallel to the belt surface (wall-parallel profiles) are presented and compared to previous measurements of profiles in a vertical plane oriented normal to the belt surface (wall-normal profiles). Additionally, photographic observations of air entrainment and measurements of air bubble size distributions and motions are reported herein. The bubble entrainment mechanisms are studied in detail through the results obtained by the DNS simulations. Free surface features resembling breaking waves and traveling parallel to the belt are observed in the wallparallel LIF movies. These free surface features travel up to 3 times faster than the free surface features moving away from the belt in the wall-normal LIF movies. These breaking events are thought to be one of the mechanisms by which the air is entrained into the underlying flow. The bubble size distribution is found to have a characteristic break in slope, similar to the Hinze scale previously observed in breaking waves (Deane and Stokes, 2002). The number of bubbles, their velocity, and size are re-ported versus depth from the experimental data. These results are qualitatively similar to results obtained by the simulations. Finally, several entrainment mechanisms are found in the simulations and their prevalence in the free surface boundary layer is assessed.

The turbulent bubble break-up cascade. Part 2. Numerical simulations of breaking waves

“…Two distinct power-law scalings emerge in two size subranges in agreement with the measurements of Tavakolinejad (2010) and Masnadi et al. (2020), which builds further confidence in the results of this work (see also Castro, Li & Carrica 2016). The size distribution is reasonably described by a scaling at intermediate sizes, which is shallower than .…”

“…10 6 4 × 10 -3 1 × 10 -2 4 × 10 -2 1 × 10 -1 resolved sizes relative to figure 6(a) (by about 3-5 times; see also figure 15) suggests that there are more small and intermediate-sized bubbles at later times, and the break-up flux from larger sizes consistently outweighs mass loss from degassing. Two distinct power-law scalings emerge in two size subranges in agreement with the measurements of Tavakolinejad (2010) and Masnadi et al (2020), which builds further confidence in the results of this work (see also Castro, Li & Carrica 2016). The size distribution is reasonably described by a D −8/3 scaling at intermediate sizes, which is shallower than D −10/3 .…”

“…The dynamics of bubble break-up appears to be distinct in the early and late wave-breaking stages, suggesting the emergence of distinct bubble generation and evolution mechanisms. The size distribution was observed to deviate from the aforementioned D −10/3 power-law scaling by Deane & Stokes (2002), Tavakolinejad (2010) and Masnadi et al (2020) late in the wave-breaking process. Prior breaking-wave simulations either did not investigate the evolution of the ensemble-averaged size distribution as a function of time, or did not conclusively recover these alternative scalings in their ensemble-averaged size distribution in the late wave-breaking stages.…”

Wake behind a three-dimensional dry transom stern. Part 1. Flow structure and large-scale air entrainment

“…As the values in table 4 represent long time averages of entrainment, turbulent breakup and buoyancy, a value β > −10/3 is expected. The slopes in table 4 are consistent with the experiments of a turbulent entraining ship hull boundary layer (β = −4.36) where multiple physical effects, including entrainment, buoyancy and turbulence, are present (Masnadi et al 2018).…”

“…The slopes in table 4 are consistent with the experiments of a turbulent entraining ship hull boundary layer ( ) where multiple physical effects, including entrainment, buoyancy and turbulence, are present (Masnadi et al. 2018).…”