Lachlan Graham

Swirling flow of viscoelastic fluids. Part 1. Interaction between inertia and elasticity

A torsionally driven cavity, consisting of a fully enclosed cylinder with rotating bottom lid, is used to examine the confined swirling flow of low-viscosity Boger fluids for situations where inertia dominates the flow field. Flow visualization and the optical technique of particle image velocimetry (PIV) are used to examine the effect of small amounts of fluid elasticity on the phenomenon of vortex breakdown. Low-viscosity Boger fluids are used which consist of dilute concentrations of high molecular weight polyacrylamide or semi-dilute concentrations of xanthan gum in a Newtonian solvent. The introduction of elasticity results in a 20% and 40% increase in the minimum critical aspect ratio required for vortex breakdown to occur using polyacrylamide and xanthan gum, respectively, at concentrations of 45 p.p.m. When the concentrations of either polyacrylamide or xanthan gum are raised to 75 p.p.m., vortex breakdown is entirely suppressed for the cylinder aspect ratios examined. Radial and axial velocity measurements along the axial centreline show that the alteration in existence domain is linked to a decrease in the magnitude of the peak in axial velocity along the central axis. The minimum peak axial velocities along the central axis for the 75 p.p.m. polyacrylamide and 75 p.p.m. xanthan gum Boger fluids are 67% and 86% lower in magnitude, respectively, than for the Newtonian fluid at Reynolds number of Re [approximate] 1500–1600. This decrease in axial velocity is associated with the interaction of elasticity in the governing boundary on the rotating base lid and/or the interaction of extensional viscosity in areas with high velocity gradients. The low-viscosity Boger fluids used in this study are rheologically characterized and the steady complex flow field has well-defined boundary conditions. Therefore, the results will allow validation of non-Newtonian constitutive models in a numerical model of a torsionally driven cavity flow.

Swirling flow of viscoelastic fluids. Part 2. Elastic effects

A torsionally driven cavity has been used to examine the influence of elasticity on the swirling flow of constant-viscosity elastic liquids (Boger fluids). A wealth of phenomena is observed as the degree of inertia, elasticity and viscous forces are varied by using a range of low- to high-viscosity flexible polyacrylamide Boger fluids and a semi-rigid xanthan gum Boger fluid. As the inertia is decreased and elasticity increased by using polyacrylamide Boger fluids, the circulation rates for a ‘Newtonian-like’ secondary flow decreases until flow reversal occurs owing to the increasing magnitude of the primary normal stress difference. For each polyacrylamide fluid, the flow becomes highly unstable at a critical combination of Reynolds number and Weissenberg number resulting in a new time-dependent elastic instability. Each fluid is characterized by a dimensionless elasticity number and a correlation with Reynolds number is found for the occurrence of the instability. In the elasticity dominated flow of the polyacrylamide Boger fluids, the instability disrupts the flow dramatically and causes an increase in the peak axial velocity along the central axis by as much as 400%. In this case, the core vortex spirals with the primary motion of fluid and is observed in some cases at Reynolds numbers much less than unity. Elastic ‘reverse’ flow is observed for the xanthan gum Boger fluid at high Weissenberg number. As the Weissenberg number decreases, and Reynolds number increases, counter-rotating vortices flowing in the inertial direction form on the rotating lid. The peak axial velocity decreases for the xanthan gum Boger fluid with decreasing Weissenberg number. In addition, several constitutive models are used to describe accurately the rheological properties of the fluids used in this work in shear and extensional flow. This experimental investigation of a complex three-dimensional flow using well-characterized fluids provides the information necessary for the validation of non-Newtonian constitutive models through numerical analysis of the torsionally driven cavity flow.

Spiral streaklines in pre‐vortex breakdown regions of axisymmetric swirling flows

In steady swirling flows in closed cylinders, it has been common to observe the transition to spirals of otherwise straight dye streaklines. This occurs in the regions where bubble type breakdown occurs but at a slightly lower Reynolds number. These regions are of particular interest for those seeking to explain the origins of vortex breakdown. The hitherto unexplained occurrence of the spiral streaklines, postulated previously to be due to non‐axisymmetry of the flow, is found to be due to small offsets of the dye injection from the central axis. The important implications of this finding are that (i) non‐axisymmetry is not a necessary route to bubble‐type vortex breakdown, and (ii) that flows displaying spiral streaklines may be still sufficiently axisymmetrical for comparison with numerical and theoretical treatments of the breakdown phenomenon.

Measurement of particle motions within tumbling granular flows.

Flowing granular materials are complex, industrially important, and scientifically provocative. In this paper we report measurements of granular transport in 3-dimensional tumbling containers. We use magnetic resonance imaging techniques for direct tracking of particles and measure the interior flows of granular materials. One goal is to measure industrial mixer performance over a wide range of conditions. As the mixer geometries are relatively simple, such measurements could serve as incisive tests during development of better granular equations of motion. (c) 1999 American Institute of Physics.

Nonmixing vortex cores in wavy Taylor vortex flow

When the symmetry of axisymmetric Taylor vortex flow is broken, time-periodic wavy vortex flow (WVF) appears and quite quickly becomes globally chaotic (in the Lagrangian sense) with increasing Reynolds number. Previously published simulations of WVF suggest that beyond a certain Re, nonmixing vortex cores reappear in the flow and grow in size with further increases in Re. This reappearance occurs well into the inertia-dominated flow regime and coincides with a decrease in axial fluid dispersion and an increase in flow symmetry as measured by certain Eulerian symmetry measures. In this brief paper, we present experimental dye-reaction visualization results from two WVF wave states in the region where vortex cores are predicted numerically. The experimental results show unambiguous visual evidence for the existence of vortex cores and provide visual agreement with the numerical results. They are significant in that experimental evidence for these structures in WVF has not been reported before. The results ...