A computational model to study the interaction of turbulence with a free-surface and its impact on air-entrainment at high Reynolds numbers

Direct numerical simulations (DNS) of forced homogeneous turbulence interacting with a free-surface can be used as a building-block configuration to reproduce most mechanisms responsible for air-entrainement and bubble generation in ship wakes. Today, however, most studies are limited to very low Reynolds numbers (i.e. Reynolds number based on the Taylor microscale of order 100), due to cost considerations. The latter comes primarily from the cost of solving the pressure Poisson equation, which has variable coefficients and cannot be solved with fast poisson solvers (FPS) based on FFTs as in the single-phase flow counterpart. In this work we propose a fractional step formulation for this class of problems which utilizes FPS. As a result the cost is significantly reduced and higher Reynolds numbers can be considered. One important aspect of the approach is the use of a conservative level-set method, which provides an efficient and accurate representation of the free-surface. The level-set technique enables the tracking of the interface between the gas and liquid phases, allowing for the study of entrainment and mixing phenomena. The solver has been validated for different 2D and 3D test cases, and the computational approach demonstrates its capability to capture the complex dynamics of free-surface turbulent flows and gas-liquid entrainment. Ensemble and spatial averages for statistical quantities such as Reynolds stresses, vorticity and volume fraction are computed and presented. Entrained bubble size distributions are compared against literature correlations.