Numerical analysis of turbulent multiphase Taylor-Couette flows

Turbulent flows involving two liquids are ubiquitous, and understanding their fundamentals is crucial for various industrial systems.
However, theoretical and experimental investigations are often challenging due to complexities such as the non-linearity of equations and interfacial dynamics.

In this dissertation, we aim to improve our understanding of two-liquid turbulent flows through interface-resolving direct numerical simulations of Taylor-Couette flows under idealised conditions.

In the first chapter, we focus on the equations and their numerical treatment to handle two-liquid and wall-bounded turbulent flows.
Specifically, we address two critical topics: the treatment of discontinuous functions, which is vital for capturing interfacial structures, and the handling of density contrasts between two liquids, essential for stable and reliable simulations of air-water flows characterised by large density differences.
The numerical methodologies are extensively validated and verified against various problems to support the subsequent discussions.

Based on these numerical methods, we investigate the dynamics of two-liquid flows in Taylor-Couette setups in the following chapters.
In the second and third chapters, we focus on two liquids with identical density and viscosity, aiming to study interactions between the free surface and characteristic secondary flow fields known as Taylor rolls.
Through qualitative and quantitative examinations, we reveal the significant impact of Taylor rolls on the concentration of the two liquids and vice versa in both turbulent and non-turbulent regimes, uncovering rich flow physics arising from the interfacial structures, turbulence, and Taylor rolls.

In the fourth chapter, we analyse two-liquid flows characterised by high density and viscosity contrasts to reveal the effects of these variations.
We find that incorporating deformable surfaces into the system can result in substantial frictional drag reduction or enhancement, which are highly dependent on the deformability of the interface.

In summary, throughout this thesis, we focus on the interfacial dynamics in Taylor-Couette flows across various parameter spaces.
Our findings clarify the importance of the interactive effects between surface deformations and the background flow fields, including Taylor rolls and turbulence.