Thesis title: 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 two problems of gas-liquid multiphase flows
occurring in natural and artificial flows.
First, we consider natural wave breaking phenomena by focusing on the
associated energy dissipation and the formation of spray, droplets, and bubbles.
The second is the breakup of liquid jets, frequently occurring in aerospace applications.
Here we focus on the atomization process, studying the formation of the droplets
and the subsequent mixing of the two phases.