Transition To Elastic Turbulence In Channel Flows

Abstract

Materials processing operations such as extrusion and coating often involve the low- inertia flow of viscoelastic fluids through straight channels. Experimental evidence suggest that such flows can transition from a laminar to a disordered flow-state, resulting in defective end-products. On the other hand, such a transition with low inertia is useful for enhancing transport in microfluidic flows where good mixing is hard to achieve. Therefore a fundamental understanding of such a transition is important. Chapter 2 of this thesis considers external disturbances in the form of small-amplitude localized body forces (impulses). They provide a good approximation of the external disturbances that can be realized relatively easily in laboratory experiments. Localized body forces are used to identify the optimal location in a channel that induces the largest kinetic energy growth. A disturbance in the channel that generates the largest kinetic energy growth has a high potential to trigger a transition to a disordered flow-state. Chapter 3 presents tools to accurately resolve steep stress gradients encountered in frequency response calculations of the linearized equations governing channel flow of a viscoelastic fluid. Recently reported well-conditioned spectral methods in conjunction with a reflection technique enable frequency response computations of channel flows of viscoelastic fluids with large elasticity. Applying the methods developed in Chapter 3 to 2D channel flow of a viscoelastic fluid, it is found that the stress can develop large magnitudes even when the velocity has negligible growth. A stress of large magnitude generated by small-amplitude disturbances may provide a new route to a transition to a disordered flow-state observed in recent experiments. Chapter 4 studies stress amplification and conditions in which they become prominent. A first step to perform direct numerical simulations (DNS) of channel flows of viscoelastic fluids using tools developed in Chapter 3 is to develop an algorithm for DNS of channel flows of Newtonian fluids. Chapter 5 extends tools discussed in Chapter 3 to perform direct numerical simulations of channel flows of a Newtonian fluid. Analyzing transition to turbulence in viscoelastic channel flows is a challenging problem that needs a multi-faceted approach involving linear and nonlinear systems theory, robust numerical methods, and complementary experiments. We believe that this dissertation provides new insights into possible mechanisms that may govern the initial stages of a transition to elastic turbulence using linear systems theory and recent numerical methods. We further hope that the numerical methods studied in this dissertation will open new avenues to simulate and analyze flow transition in complex fluids.