A novel three-phase mixture approach for the numerical modeling of self-aerated flows

Abstract

This work presents a novel theoretical/numerical model for the simulation of self-aerated flows under a Reynolds-Averaged Navier-Stokes (RANS) framework. The new formulation is based on a three-phase mixture approach composed of a continuous air phase, a bubble phase, and a continuous water phase. A mass transfer mechanism that does not depend on an entrainment function and does not require calibration accounts for the incorporation of air into the flow. A modification in the formulation of the Volume-of-Fluid algorithm (used to track the free surface) allows one to capture the increase in water depth due to the presence of bubbles. The proposed formulation recovers the traditional Volume-of-Fluid formulation for free surface flows in the absence of bubbles, allowing the model to represent simultaneously the aerated and not aerated regions of a flow. Governing equations for the mixture are derived from mass and momentum conservation equations for each phase, and a numerical algorithm that ensures the boundedness of the numerical solution is proposed. The model is tested and validated using four experimental cases: a degassing tank, a bubble plume, a plunging jet, and a stepped spillway, showing very satisfactory results. The new methodology provides a significant advance in the current capabilities for simulating self-aerated flows.