Spatio-temporal mode dynamics and higher order transitions in high aspect ratio Newtonian Taylor–Couette flows

Abstract

Spatial and temporal frequency dynamics were experimentally tracked via flow visualization for Newtonian fluids as a function of the inner cylinder Reynolds number (Rei) in the flow between concentric, independently rotating cylinders with a radius ratio of 0.912 and an aspect ratio of 60.7. Eight transitions from laminar to turbulent flow were characterized in detail for a stationary outer cylinder, producing highly resolved space–time and frequency–time plots for wavy, modulated and weakly turbulent states. A previously unreported early-modulated wavy vortex flow was found in our high aspect ratio geometry both with and without the presence of a dislocation. The envelope of stability for this flow state was shown to cross into the co-rotating regime, and is present up to Reo ~ 60, where Reo is the outer cylinder Reynolds number. This early modulation is independent of acceleration in the range 0.18 < dRei/dτ < 2.9, where τ is the time nondimensionalized with a viscous time scale. While many of the flow states have been previously observed in geometries with somewhat different radius ratios, we provide new characterization of transitional structures for Reo = 0 in the range 0 < Re* < 21.4, where Re* = Rei/Rec and Rec is the value of Rei at the primary instability. Special attention has been given to ramp rate. For quasi-static ramps, axisymmetric states are stable over the ranges of Re* = [(0–1.17), > 15.4], states characterized by a single distinct temporal frequency for Re* = [(1.17–1.41), (3.56–5.20), (7.85–15.4)], states with multiple temporal frequencies for Re* = [(1.41–3.56), (5.20–7.85)], and a transition from laminar to weakly turbulent vortices occurs at Re* = 5.49. All flow states are characterized by symmetry/symmetry-breaking features as well as azimuthal and axial wavenumbers.

Experimental investigation of mixing and axial dispersion in Taylor–Couette flow patterns

“…The non-uniqueness of flow (Coles 1965;Rudman 1998;Dutcher and Muller 2009) was also observed through the existence of hysteresis phenomena. Multiple stable flow states could be reached for a given Reynolds number.…”

“…A ramp generator controls the rotor acceleration during transient evolution to the desired Reynolds number. Indeed, for the same Reynolds number, Re, using different acceleration ramps provides various flow states (Dutcher and Muller 2009). Therefore, a given wave regime is selected by following one of the prescribed start-up protocols.…”

Mixing and axial dispersion in Taylor–Couette flows: The effect of the flow regime

“…A ramp generator controls the rotor acceleration during the transient evolution to the desired Reynolds number. Indeed, as highlighted by Coles [7] and Dutcher and Muller [30], for a given Reynolds number, the use of different acceleration ramps may lead to various flow states. Therefore, for the two configurations under study, different wave regimes were reproducibly achieved by selecting one of the following start-up protocol:…”

Polymer and Particle Dynamics and Assembly in Varied Hydrodynamic Fields

“…A bifurcation in the flow state is determined by a change, loss, or generation of a characteristic peak in either the spatial or temporal frequency spectra. Further details about the geometry and visualization can be found elsewhere . For reference, the flow state shown in Figure is the primary instability, called Taylor vortex flow.…”

“…For Re o = 0, η = 0.912, and Γ = 60.7, the flow states observed with increasing Re i include Couette flow; axisymmetric vortices (Taylor vortex flow, TVF); nonaxisymmetric vortices (wavy vortex flow, WVF, and modulated wavy vortex flow, MWV); and finally weakly turbulent flow states (chaotic wavy vortex flow, CWV, wavy turbulent vortex flow, WTV, and turbulent Taylor vortex flow, TTV). When Re o is nonzero, additional states, including spiraling states, are accessible (Figure a) . Therefore, for Newtonian TC flows, the critical Reynolds number, Re c , defining the onset of a flow state based on the inner cylinder Re i , is a function of η , Γ , and Re o .…”