Numerical simulation and prediction of non-Newtonian fluid flows

QC260317

Abstract

Non-Newtonian fluids such as viscoelastic and elastoviscoplastic (EVP) materials are ubiquitous in industrial and environmental flows and exhibit complex rheological behavior that alters flow topology across multiple scales in comparison to Newtonian liquids. Their dynamics are governed by additional elastic and plastic stresses, which crucially affect the regimes of interfacial processes and turbulent flows. This thesis investigates how elasticity and yield stress jointly influence multiphase and canonical wall-bounded flows, and how data-driven methods can be used to infer experimentally inaccessible stress fields. The study is based on direct numerical simulations (DNSs) of viscoelastic and EVP flows, along with baseline convolutional neural networks for non-intrusive sensing in turbulent configurations.

We first investigate the effects of complex rheology on the dynamics of an interface in an EVP material when a bubble bursts on the surface, where the driving mechanism is the capillary stress. The numerical simulation of bubble bursting uncovers how the elastic stresses and their relaxation interacts with the yield stress. The parameter space in the study is spanned by the Deborah number and plasto-capillary number. Four distinct regimes are identified, ranging from Newtonian-like jetting to yield-dominated states with limited jet formation.

Then, we examine what happens when a viscoelastic droplet of polyacrylamide solution impacts a super-hydrophobic surface at high speed. The experimental investigation reveals that, in contrast to previous studies, viscoelastic droplets may experience full rebound while Newtonian droplets do not. This happens through a balloon regime in which the impacting droplet first impales the surface and the rebounding droplet forms a thin ligament which later rebounds together with the drop, like a rubber band. The regime arises from the combined effect of substrate characteristics, liquid impalement and strong polymeric stresses that prevent ligament breakup. Using DNS, we show that such a regime is reproduced numerically, provided sufficient modeling of the contact line behavior. Using a simplified theoretical framework we propose a necessary condition for the complete droplet rebound. In the splashing regime of Newtonian fluids, viscoelastic drop impact is shown to exhibit elongated fingers. Increasing polymer concentration enhances viscous damping, reducing the number of fingers and eventually suppressing fingering instabilities while preserving complete rebound. The onset and evolution of fingering are a result of the competition between inertia--capillary--viscous terms, and a theoretical framework is shown to predict the temporal growth of the characteristic ligament length across rheological conditions.

We then turn to a chaotic flow regime, and study elastoviscoplastic channel flow at low Reynolds numbers (Re=5-500), where viscoelastic fluids display elasto-inertial turbulence ("early turbulence"). We demonstrate that the presence of yield stress does not relaminarize the flow unlike in inertial turbulence at high Reynolds numbers. Further, we show that the EVP stresses transition from net sinks to net sources of turbulent kinetic energy as elasticity of the material is increased.

Since the turbulent nature of non-Newtonian fluid flows require description of both the flow and extra stresses, where the latter is not accessible in experiments, we develop a methodology to retrieve the velocity and elastic stress fields in viscoelastic turbulent channel flows from wall measurements. We show that the introduced baseline methodology can learn highly non-linear mapping between wall information and near-wall flow and stress fields but also is limited by the accurate retrieval of small scale structures. Towards enhancing the performance of the non-intrusive sensing methodology in an experimental setting, we introduce spectrally informed loss functions which are tested in a Newtonian fluid flow configuration as a part of this thesis work and will be extended to non-Newtonian configurations. Taken together, the findings in the present thesis provide an idea of the behavior of complex fluids in different configurations, while demonstrating the potential of data-driven techniques to estimate inaccessible stress fields in non-Newtonian turbulence.

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