Numerical Methods for Non-Newtonian Fluids
Numerical Methods for Non-Newtonian Fluids

Author:

Publisher: Elsevier

Published: 2010-12-20

Total Pages: 826

ISBN-13: 0080932029

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Non-Newtonian flows and their numerical simulations have generated an abundant literature, as well as many publications and references to which can be found in this volume's articles. This abundance of publications can be explained by the fact that non-Newtonian fluids occur in many real life situations: the food industry, oil & gas industry, chemical, civil and mechanical engineering, the bio-Sciences, to name just a few. Mathematical and numerical analysis of non-Newtonian fluid flow models provide challenging problems to partial differential equations specialists and applied computational mathematicians alike. This volume offers investigations. Results and conclusions that will no doubt be useful to engineers and computational and applied mathematicians who are focused on various aspects of non-Newtonian Fluid Mechanics. - New review of well-known computational methods for the simulation viscoelastic and viscoplastic types - Discusses new numerical methods that have proven to be more efficient and more accurate than traditional methods - Articles that discuss the numerical simulation of particulate flow for viscoelastic fluids

Flow Behavior and Instabilities in Viscoelastic Fluids
Flow Behavior and Instabilities in Viscoelastic Fluids

Author: Boyang Qin

Publisher:

Published: 2018

Total Pages: 0

ISBN-13:

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The flow of complex fluids, especially those containing polymers, is ubiquitous in nature and industry. From blood, plastic melts, to airway mucus, the presence of microstructures such as particles, proteins, and polymers, can impart nonlinear material properties not found in simple fluids like water. These rheological behaviors, in particular viscoelasticity, can give rise to flow anomalies found in industrial settings and intriguing transport dynamics in biological systems. The first part of my work focuses on the flow of viscoelastic fluids in physical systems. Here, I investigate the flow instabilities of viscoelastic fluids in three different geometries and configurations. Realized in microfluidic channels, these experiments mimic flows encountered in technology spanning the oil extraction, pharmaceutical, and chemical industries. In particular, by conducting high-speed velocimetry on the flow of polymeric fluid in a micro-channel, we report evidence of elastic turbulence in a parallel shear flow where the streamline is without curvature. These turbulent-like characteristics include activation of the flow at many time scales, anomalous increase in flow resistance, and enhanced mixing associated with the polymeric flow. Moreover, the spectral characteristics and spatial structures of the velocity fluctuations are different from that in a curved geometry. Measured using novel holographic particle tracking, Lagrangian trajectories show spanwise dispersion and modulations, akin to the traveling waves in the turbulent pipe flow of Newtonian fluids. These curvature perturbations far downstream can generate sufficient hoop stresses to sustain the flow instabilities in the parallel shear flow. The second part of the thesis focuses on the motility and transport of active swimmers in viscoelastic fluids that are relevant to biological systems and human health. In particular, by analyzing the swimming of the bi-flagellated green algae Chlamydomonas reinhardtii in viscoelastic fluid, we show that fluid elasticity enhances the flagellar beating frequency and the wave speed. Yet the net swimming speed of the alga is hindered for fluids that are sufficiently elastic. The origin of this complex response lies in the non-trivial change in flagellar gait due to elasticity. Numerical simulations show that such change in gait reduces elastic stress build up in the fluid and increases efficiency. These results further illustrate the complex coupling between fluid rheology and swimming gait in the motility of micro-organisms and other biological processes such as mucociliary clearance in mammalian airways.

The Effects of Viscoelasticity on the Transitioning Cylinder Wake
The Effects of Viscoelasticity on the Transitioning Cylinder Wake

Author: David Hastings Richter

Publisher: Stanford University

Published: 2011

Total Pages: 166

ISBN-13:

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Using a newly developed three dimensional, time dependent finite volume code designed to compute non-Newtonian flows over a large range of Reynolds number (Re), we performed simulations of viscoelastic flow past a circular cylinder. Our goal was to elucidate elastic effects during transition to turbulence in a bluff body wake. Based on its ability to capture essential physical processes in turbulent drag reduction studies, the FENE-P rheological model was employed in the calculation, and the numerical method utilized was such that a large range of rheological parameters (polymer length L, dimensionless Weissenberg number (Wi), and polymer concentration (beta) in the FENE-P model) could be probed. Simulations were performed for Reynolds numbers ranging from Re = 100 to Re = 3900. Within this range, the Newtonian cylinder wake first undergoes a series of secondary instabilities, transitioning the wake structure from a two-dimensional, laminar vortex shedding state to one exhibiting three-dimensional motion. This transition is characterized first by the mode A instability, which develops in the region of primary vortex development at a Reynolds number of Re = 190. The mode B instability then follows at Re = 260, resulting from unstable perturbation growth in the braid region between primary vortices. At still higher Reynolds numbers, Re = O(1000), the separated shear layer immediately behind the cylinder begins to transition prior to primary vortex shedding. Through nonlinear simulations as well as a Floquet linear stability analysis, viscoelasticity was observed to stabilize both regimes of three-dimensional transition. Full nonlinear simulations revealed that for high enough polymer extensibility L at Re = 300, where mode B instability structures dominate for Newtonian flow, the wake could be reverted back to a state resembling two-dimensional, laminar vortex shedding. This was then confirmed using a Floquet stability analysis, showing significantly suppressed growth rates for both the mode A and mode B instabilities in the linear regime of their development. Mechanisms of this stabilization are presented. At Re = 3900, viscoelasticity again stabilizes the flow, though at this point through a suppression of the Kelvin-Helmoltz rollup instability present in the separated shear layer for Newtonian flows. Once a primary Karman vortex is allowed to form without the influence of a transitioned shear layer, the wake then reverts back to one resembling the mode B instabilities. Confirming this, a study was then performed at the same Reynolds number but allowing for an inhomogeneous polymer concentration throughout the flow field. By injecting polymer additives on the upstream side of the cylinder, it was found that stabilization of the shear layer and of the subsequent wake could be achieved without the presence of polymeric stresses in all downstream locations of the flow.