Numerical Analysis of Turbulent Multiphase Taylor–Couette Flows
Naoki Hori is a PhD student in the Department Physics of Fluids. Promotors are prof.dr. D. Lohse and prof.dr. R. Verzicco of the Faculty of Science & Technology.
Turbulent flows consisting of two liquids are omnipresent, and understanding their fundamentals is crucial for enhancing the efficiency of various industrial systems. However, theoretical or experimental investigations are often challenging due to the complexity arising from the non-linearity of equations, interfacial dynamics, surfactants, and chemical components. In this dissertation, by means of interface-resolving direct numerical simulations of Taylor-Couette flows under idealised conditions, we aim to improve our understanding of two-liquid turbulent flows.
In the first chapter, we focus on the equations and their numerical treatment to handle two-liquid and wall-bounded turbulent flows. Specifically, we discuss two crucial topics: the treatment of discontinuous functions, which is pivotal for capturing interfacial structures, and the treatment of density contrasts between two liquids, which is essential for stable and reliable simulation of air-water flows characterised by large density differences. The numerical methodologies are extensively validated and verified against various problems to solidify the subsequent discussions.
Based on the numerical methods, we investigate the dynamics of two-liquid flows in Taylor-Couette setups in chapters 2, 3, and 4.
In the second chapter, we focus on two liquids having identical density and viscosity in a low Reynolds number, aiming at studying interactions between the free surface and characteristic secondary flow fields known as Taylor rolls, in the absence of turbulence. We find nonlinear effects of the interfacial structures, mainly due to the different deformability of the free surface. In particular, we find that less-deforming interfacial structures are so stiff that they modulate the Taylor rolls, resulting in a highly nonlinear torque response. Through qualitative and quantitative examinations, we reveal how interfacial structures influence the flow fields and vice versa.
Building on the discussion in the second chapter, we incorporate the effects of turbulence in the third chapter. Among other observations, we note a clear effect of Taylor rolls on the concentration of the two liquids: easily deformable surfaces lead to well-mixed states, while less deformable surfaces strongly transport the dispersed phase to the centre of the rolls. By quantifying the deformation of droplets, we also reveal how droplet morphologies differ in the bulk and in the near-wall region, another clear consequence of the Taylor rolls.
To reveal the effects of density and viscosity variations which are omitted in the previous chapters, we shift our focus to two-liquid flows characterised by high density and viscosity contrasts in the fourth chapter. In addition to various parameters explored in the previous chapters, we consider two different wall-bounded domains (plane-Couette and Taylor-Couette setups) to shed light on their effects.
We find that easily deformable surfaces result in substantial frictional drag reduction, attributed to air forming layered structures on the wall, which attenuates turbulence. Conversely, we observe that less deformable surfaces hardly influence drag or may even increase it, due to bubbly structures disturbing flow fields and enhancing momentum transport. In addition to this mechanism, which is clearly observed in plane-Couette setups, we identify a typical phenomenon in Taylor-Couette setups where Taylor rolls interfere with the formation of layered air, affecting drag modulation.
In summary, throughout the thesis, we focus on the interfacial dynamics in Taylor-Couette flows for various parameter spaces, which hopefully clarify the importance of the interactive effects between surface deformations and the background flow fields, including Taylor rolls and turbulence.
