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

Jack R. C. King, Steven J. Lind, Benedict D. Rogers, Peter K. Stansby, Renato Vacondio

Published 2022-06-03Version 1

For turbulent bubbly flows, multi-phase simulations resolving both the liquid and bubble phases are prohibitively expensive in the context of practical engineering design. One such example is breaking waves, where the presence of bubbles plays a role in wave impact loads, acoustic emissions, and atmospheric-ocean transfer, but detailed simulations in all but the simplest settings are infeasible. An alternative is to resolve only the large scales, and model small scale bubbles, which may be represented as a set of discrete particles. Here we introduce a large eddy simulation (LES) Smoothed Particle Hydrodynamics (SPH) scheme for simulations of bubbly flows with free-surface. The continuous liquid phase is resolved with a semi-implicit isothermally compressible SPH framework. This is coupled via a discrete Lagrangian bubble model: bubbles and liquid interact via exchanges of volume and momentum, and through turbulent closure, bubble breakup and entrainment, and free-surface interaction models. By representing bubbles as discrete particles, they can be tracked over their lifetimes, allowing closure models for sub-resolution fluctuations, bubble deformation, break-up and free-surface interaction to be constructed in integral form, accounting for the finite timescales over which these events occur. We use our framework to investigate two flows: bubble plumes, and breaking waves, and find close quantitative agreement with published experimental and numerical data. In particular, for breaking waves, our framework accurately predicts the Hinze scale, the bubble size distribution and growth rate of the entrained bubble population for plunging breakers. This is the first coupling of an SPH framework with a discrete bubble model (that we are aware of), and has potential for cost effective simulations of wave-structure interactions with more accurate predictions of wave impact loads.