Phase-field simulations of two-phase pipe flow

Phase-field approaches have emerged as a promising tool to model the flow of immiscible
fluids in recent years. Their ability to naturally capture interface topological
changes is widely recognized, but their accuracy in simulating flows of real fluids in
practical geometries is not well established.
The main aim of this thesis was to develop and test a novel method for the accurate
modelling of two-phase flows in pipes based on a diffuse phase-field model.
In this model, the Cahn-Hilliard-Navier-Stokes equations are solved in cylindrical
coordinates with a pseudo-spectral discretization. The corresponding computer
implementation was carried out in this thesis and includes a hybrid OMP-MPI parallelization
strategy that shows good scalability up to several thousand cores. The new
computer code was used to investigate quantitatively the convergence of the phasefield
method toward the sharp-interface limit in a variety of cases. Furthermore,
linear stability analysis and three-dimensional direct numerical simulations (DNS)
were carried out to study the evolution of a mixture of real fluids, namely kerosene
and water, under realistic laboratory conditions at a moderate Reynolds number.
For a specific parameter set, the simulations show that the mixture relaxes into a turbulent
slug flow regime provided that the pipe is sufficiently long. This configuration
presents mild turbulence and large scale three-dimensional recirculation patterns. In
summary, this thesis demonstrates the capabilities of phase-field methods to reliably
simulate two-phase flows and shows they can be used to explore the complex regime
maps typical of multiphase flows and to accurately characterize the resulting flow
configurations.