Multiscale modeling of turbulence and bubbles in two-phase flows

Environmental and engineering two-phase flows, such as those encountered in oceanic, coastal, and industrial systems, exhibit a range of spatial and temporal scales. These flows may involve surface waves with wavelengths on the order of meters while simultaneously containing gas bubbles with radii on the order of micrometers, posing significant challenges for direct numerical simulations. We present a robust and efficient multiscale numerical solver designed for simulating complex two-phase flows involving turbulence and bubble dynamics. Our approach integrates advanced numerical techniques with recent developments in turbulence modeling and bubble population dynamics, enabling the simulation of flows characterized by large variations in length and time scales. The continuous phases (air and water) are captured using an interface-resolved coupled level set and volume-of-fluid (CLSVOF) method. Turbulence is modeled using the Reynolds-averaged Navier–Stokes (RANS) framework, with the k–ω closure employed to model the effects of turbulence on the mean flow. Subgrid-scale bubbles are represented through a population balance model (PBM) that evolves the bubble size distribution over time by incorporating key physical processes, including bubble entrainment, bubble fragmentation, and bubble coalescence. To ensure numerical stability, the RANS equations are solved using a mass-momentum-consistent discretization scheme that can handle high density ratios and large void fractions, typical conditions observed in realistic air–water systems. We demonstrate the capabilities of our solver through a series of canonical test cases and breaking waves of various wave steepness. Particular focus is given to the evolution of the bubble size distribution during the active wave breaking phase and the subsequent degassing dynamics once breaking subsides.