Development of a gas–liquid multiphase solver for direct numerical simulation of atomization phenomena

Gas-liquid multiphase flows play an essential role in nature and industry. Understanding the complex dynamics of multiphase flows is fundamental in many technological applications, including metal forming and energy production industries. In aerospace applications, multiphase flows have considerable importance in the atomization and mixing of fuels, as well as in sloshing in fuel tanks. In nature, one of the most complicated and important phenomena is the breaking of waves, in which complex atomization processes occur, leading to the formation of bubbles, droplets, spray, and aerosol. In this thesis work, we develop an efficient solver for direct numerical simulation of the incompressible Navier-Stokes equations to study multiphase flow phenomena as bubble dynamics and formation, and atomization phenomena, in both natural and artificial flows. In the first part of the thesis, we present the basic equations that govern multiphase flow dynamics within the one-fluid formulation approach. The solver relies on the Volume-of-Fluid (VOF) method to account for different phases, and the interface tracking is carried out using novel schemes based on a tailored TVD limiter. A staggered Cartesian mesh is used, and space derivatives approximated with second-order finite-difference formulas to guarantee discrete energy preservation. Moreover, for time integration, Adams-Bashfort extrapolation is used for the convective terms and interface tracking, whereas implicit Crank-Nicolson time integration is used for the viscous terms. Surface tension is accounted for through the continuous surface force (CFS) approach, and the local interface curvature is approximated through a hierarchical approach, whereby the height function method is locally replaced with least-square derivative estimation at critical points. Several validation test cases are then presented. First, capillary wave motion and bubble in a shearing field are studied to validate surface tension discretization. Second, the dynamics of a rising bubble in a liquid tank are presented, and the results are compared with other authors. Finally, we analyze the physics of gas-liquid multiphase flows occurring in natural flows. We consider natural wave breaking phenomena by focusing on the associated energy dissipation and the formation of spray, droplets, and bubbles.