2 results
Swirling flow of viscoelastic fluids. Part 2. Elastic effects
- JASON R. STOKES, LACHLAN J. W. GRAHAM, NICK J. LAWSON, DAVID V. BOGER
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- Journal:
- Journal of Fluid Mechanics / Volume 429 / 25 February 2001
- Published online by Cambridge University Press:
- 01 March 2001, pp. 117-153
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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.
Swirling flow of viscoelastic fluids. Part 1. Interaction between inertia and elasticity
- JASON R. STOKES, LACHLAN J. W. GRAHAM, NICK J. LAWSON, DAVID V. BOGER
-
- Journal:
- Journal of Fluid Mechanics / Volume 429 / 25 February 2001
- Published online by Cambridge University Press:
- 01 March 2001, pp. 67-115
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- Article
- Export citation
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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 ≈ 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.