Turbulent flows of generalized Newtonian fluids: mechanics and structural coherence

Abstract

Most flows are turbulent in nature, yet fluids exhibit a plethora of inherent responses to applied stress. Fluids that respond in a linear manner, such as water and air, are labelled as Newtonian, whereas the majority of them that do not are often called non-Newtonian. Some of these fluids show instantaneous deformation in directions perpendicular to the applied stress, others present elastic recovery, or yield-stress (plasticity), and some even flow more easily under increasing shear stress. The latter, a type of shear-dependent rheology known as shear-thinning or pseudoplastic behaviour, is one of the most common non-Newtonian fluid behaviours in numerous industrial settings. Consequently, the understanding of turbulent flows of these fluids; i.e., those exhibiting sheardependent rheology, is fairly important for a good number of engineers and scientists. The present thesis is concerned with the investigation of turbulent flows corresponding to generalized Newtonian (GN) fluids. The aim is to study the mean-flow properties, and the features of some coherent structures; more specifically, turbulent vortices. For this purpose, the numerical simulations of two distinct flows are considered: turbulent channel flow, and turbulent flow in a baffled stirred tank with a Rushton-type impeller. Here, a GN fluid refers to an idealization of a real fluid presenting shear-dependent rheology as its most characteristic rheological feature. GN fluids are modelled through a so-called constitutive equation, where the response to stress is made proportional to it through a material function (apparent shear viscosity) depending on the rate of deformation. In this work, the Carreau model is selected to incorporate the GN fluid rheology into the momentum equation. Key accomplishments of this thesis include: (i) the displaying of drag reducing features in turbulent channel flow for a slight-to-moderate degree of shear-thinning, even in the absence of other non-Newtonian behaviours (e.g., extensional thickening, or elastic effects); (ii) the discovery of qualitative similarities between turbulent pipes and turbulent channels of GN fluids, which hints to the possibility of having a universal near-wall behaviour for these internal flows even after complex effects are introduced; (iii) the analysis of quasi streamwise vortices, and of the near-wall self-sustaining process in turbulent channel flow of a shear-thinning fluid; (iv) the presentation of the mean momentum balance analysis (see, e.g., Klewicki, 2013) for turbulent channel flow of GN fluids; (v) the study of turbulent vortices in a baffled stirred tank with (potential) important implications for dispersed systems; among other findings.