Numerical Simulation Of The Transition To Elastic Turbulence In Viscoelastic Inertialess Flows

Numerical Simulation of the Transition to Elastic Turbulence in Viscoelastic Inertialess Flows

Fluid mixing represents an important component of the field of fluid dynamics, what makes the understanding of this subject so meaningful from both the fundamental and applied (e.g. industrial processes) point of view. In miniaturised geometries, under typical conditions, mixing is a slow, difficult and inefficient process due to the naturally laminar character of these flows, which forces the homogenisation of different fluid elements to occur via molecular diffusion instead of faster-acting advective transport. However, recent experimental studies on low-Reynolds-number viscoelastic flows have shown that efficient mixing can be triggered in several geometrical configurations (including micro-scale devices), by the phenomenon of elastic turbulence. The first part of this thesis is devoted to the understanding and investigation of numerical challenges present in the domain of non-Newtonian fluid dynamics, focusing in particular on the high-Weissenberg number problem. The latter manifests as a breakdown of the numerical scheme when the polymeric extra-stress evolution equations are implemented in a direct way, which poses severe limits to the possibility to accurately simulate elastic turbulent flows. We provide numerical evidence of the beneficial effect (in terms of increased stability) of the square-root decomposition of the extra-stress in a finite-volume-based implementation of the governing equations in a two-dimensional channel. The second part of the thesis reports about the emergence and characterisation of purely-elastic instabilities in numerical simulations of zero-Reynolds-number Oldroyd-B fluids in a two-dimensional cross-slot geometry. By means of extensive numerical work, we provide a detailed characterisation of the purely-elastic instabilities arising in the system for wide ranges of both the fluid elasticity and the polymer concentration. For concentrated solutions and large enough Weissenberg numbers, our simulations indicate the emergence of disordered flow pointing to elastic turbulence. We analyse the transition to irregular dynamics and characterise the statistical properties of such highly elastic flows, discussing the similarities and differences with experimental results from the literature.

Applied Mechanics Reviews

Dissertation Abstracts International