A sub-grid air entrainment model for breaking bow waves and naval surface ships

Direct numerical simulations (DNS) of air entrainment by the breaking bow waves of naval surface ships are outside of the computational reach of the most powerful computers in the foreseeable future. This creates a need for physically-based models of air entrainment for applications in numerical simulations for ship design. Due to the non-linear dependence of the terminal bubble velocity with diameter most air entrainment flows have a high void fraction region immediately below the free surface. We present a model that locates this region employing the local liquid velocity and the distance to the interface. Using this model and the bubble size distributions measured by Deane and Stokes [Deane BD, Stokes MD. Scale dependence of bubble creation mechanisms in breaking waves. Nature 2002;418:839-44] we have simulated the air entrainment in the breaking wave experiments of Wanieski et al. [Waniewski TA, Brennen CE, Raichlen F. Measurement of air entrainment by bow waves. J Fluids Eng 2001;123:57-63]. Comparison against these experimental data is good. We then apply this model to simulate the flow around naval combatant DTMB 5415 and the research vessel Athena. The model predicts air entrainment in regions where it was actually observed at sea, namely the breaking bow wave, along the water/air/hull contact line and in the near-wake. To the best of our knowledge this is the first model of air entrainment that compares favorably with data at laboratory scale and also presents the right trends at full-scale.