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For turbulent bubbly flows, multi-phase simulations resolving both the liquidand bubbles are prohibitively expensive in the context of different naturalphenomena. One example is breaking waves, where bubbles strongly influence waveimpact loads, acoustic emissions, and atmospheric-ocean transfer, but detailedsimulations in all but the simplest settings are infeasible. An alternativeapproach is to resolve only large scales, and model small scale bubblesadopting sub-resolution closures. Here we introduce a large eddy simulation(LES) Smoothed Particle Hydrodynamics (SPH) scheme for simulations of bubblyflows. The continuous liquid phase is resolved with a semi-implicitisothermally compressible SPH framework. This is coupled with a discreteLagrangian bubble model. Bubbles and liquid interact via exchanges of volumeand momentum, through turbulent closures, bubble breakup and entrainment, andfree-surface interaction models. By representing bubbles as individualparticles, they can be tracked over their lifetimes, allowing closure modelsfor sub-resolution fluctuations, bubble deformation, breakup and free-surfaceinteraction in integral form, accounting for the finite timescales over whichthese events occur. We investigate two flows: bubble plumes, and breakingwaves, and find close quantitative agreement with published experimental andnumerical data. In particular, for plunging breaking waves, our frameworkaccurately predicts the Hinze scale, bubble size distribution, and growth rateof the entrained bubble population. This is the first coupling of an SPHframework with a discrete bubble model, with potential for cost effectivesimulations of wave-structure interactions and more accurate predictions ofwave impact loads.

Large Eddy Simulations of bubbly flows and breaking waves with Smoothed Particle Hydrodynamics