Experimental investigations into the transitions to turbulence in Newtonian and drag-reducing polymeric Taylor-Couette flows

This dissertation reports on the quantification of flow transitions for Newtonian and dilute drag-reducing polymer solutions in flow between concentric, rotating cylinders (Taylor-Couette flow). Flows transition to turbulence through a series of intermediate states of gradually increasing complexity in the Taylor-Couette (TC) flow geometry. This study harnesses the TCs unique geometry to examine flow-stability modifications of isolated flow states due to a polymeric additive. We have mapped the stability boundaries of multiple flow regimes in a TC geometry of radius ratio 0.912 and aspect ratio 60.7 using Newtonian fluids and five dilute polyethylene oxide solutions in glycerin/water. The elasticity of the PEO solutions, El, defined as the ratio of the polymer relaxation time to the viscous time scale, ranges from O(0.0001 to 1). We have discovered that the effect of the polymeric additive is mode-dependent, meaning the polymeric solutions uniquely stabilize or destabilize each distinct flow type in the TC flow. Also, in general, with increasing elasticity, modifications of the flow structure occur, with higher-order flow states modified at lower levels of elasticity, and changes to lower-order flow states occurring at higher levels of elasticity. With this knowledge, optimal solution properties for drag reducing agents to be used in a specific application may be identified, which could result in sizeable energy and cost saving benefits related both to transport of fluids and transport through fluids.;Changes in stability were measured with Reo held constant during adiabatic increases of Rei using flow visualization in 2D planes of radial, axial, projected azimuthal and time dimensions, where Reo,i is the Reynolds number based on the outer or inner cylinder, respectively. In order to quantify the evolution of both temporal and spatial frequencies throughout the sequence of transitions, we have developed a novel methodology that quantifies the time-dependent temporal and spatial spectral profile of multiple flow states as the flow transitions from laminar to turbulent flow. For the El = 0, Newtonian TC problem, this methodology has allowed us to discover new stable flow states, such as early modulated wavy vortex flow (MWV1), as well as identify the critical conditions that were previously unreported. For adiabatic ramps, axisymmetric states are stable over the ranges of Re* = [(0--1.17), >15.4], single temporal frequencies for Re* = [(1.17--1.41), (3.56--5.20), (7.85--15.4)], multiple temporal frequencies for Re* = [(1.41--3.56), (5.20--7.85)1, and a transition from laminar to weakly turbulent vortices occurs at Re* = 5.49 where Re* = Rei/Re c and Rec is the value of Re i at the primary instability. In addition, for the first transition from the base flow, we have developed explicit analytic formulae for the critical conditions that collapse all existing data over the entire range of radius and rotation ratios.;For the non-Newtonian TC problem, the effect of elasticity was found to be mode-dependent, meaning that the extent of stability boundary stabilization or destabilization depends on the flow type. The presence of the polymer tended to generally stabilize single temporal frequency states (e.g. wavy vortex flow) and destabilize coherent axisymmetric states (e.g. turbulent Taylor vortex flow) in the El << 1 regime. The effect of El was also found to be non-monotonic for some states (e.g. Taylor Vortex Flow). The modifications of critical conditions for flow states with chaotic inner-vortex motion (20%--200%) were more significant than laminar vortex flows (∼5%). For the El → 1 non-Newtonian TC problem, the sequence of transitions was notably altered and the transition to a 'turbulent' state occurred at an order of magnitude lower Rei. Laminar flow and elastic turbulence were only separated by two coherent states, stationary vortices and disordered rotating standing waves.