Session X37: Non-Newtonian Flows: Turbulence & Instabilities

Influence of shear-thinning fluid on vortex formation in pulsatile, turbulent flow

Vortex formation in shear-thinning fluids is an important research topic due to their ubiquity in biological and engineering contexts. Vortices formed in shear-thinning fluids have been shown to possess lower circulation, propagate a smaller distance, and have reduced local strain rates compared to those formed in Newtonian fluids (Palacios-Morales and Zenit, 2013). The presence of vortical structures affects the overall macro characteristics of the flow such as fluid mixing and drag. In the present work, we have investigated these structures using time-resolved PIV measurements in a pulsatile flow loop experiment, comparing both a xanthan gum shear-thinning fluid and a Newtonian fluid. The field of view is downstream a stenosis model designed to create vortical structures when the flow loop is operated in a pulsatile manner to produce unsteady and very unsteady flows. The parameter space includes transitional to turbulent mean Reynolds numbers and non-negligible Strouhal numbers. Steady cases at the respective mean Reynolds numbers are tested for comparison. Flow field analysis has been carried out to elucidate the differences between the two fluids where it is predicted that the viscoelastic properties of the xanthan gum affects the flow physics and could reduce mixing.   

Lundgrens Infinite Hierarchy of Probability Density Functions for Linear Viscoelastic Materials

The statistical theory of inertial turbulence at high Reynolds numbers has been well-established and thoroughly studied for the better part of a century. The treatment in terms of multi-point probability density functions, governed by Lundgren's infinite hierarchy of transport equations, is particularly tractable.

The governing equations have recently been extended to the treatment of compressible flows, and the treatment of active- and magnetohydrodynamic turbulence. However, no such description of viscoelastic turbulence yet exists.

To obtain a formally closed description of viscoelastic turbulence, the introduction of multi-time probability density functions is proposed, capturing the temporally non-local nature of the Cauchy stress tensor. These density functions convey the probability of observing the velocities v₁ through v_N at N separate spatiotemporal points, within some infinitesimal phase-space volumes dv_i. Finally, a Lungren-type hierarchy is obtained by utilizing the deterministic one-point momentum equations. Although the current framework only allows for the treatment of linear viscoelastic materials, its extension to the more general Walter’s fluids is discussed.   

Fracturing instability in interfacial Hele-Shaw flows involving complex fluids

Fracturing instability has been observed in experiments on interfacial Hele-Shaw flows involving at least one complex fluid but there has not been much theoretical work on the origin of this instability. In this talk, we will discuss this problem by setting it up as a linear stability problem where a viscous Newtonian fluid (or air) displaces an Oldroyd-B (OB) fluid in a rectilinear Hele-Shaw cell. Results of such an analysis shows that compared to upper convected maxwell (UCM) case, a certain regularizing effect of the Newtonian contribution of the stress from OB is found, (i) at least one of the singular behaviors found in UCM case is removed, and (ii) less unstable than the UCM case. This is a joint work with Zhiying Hai. 

Note: A similar version of this talk was scheduled in the program of last year for remote delivery in Indianapolis but could not be delivered because of internet problems.   

The polymer diffusive instability in high concentration polymer solutions

Numerous mechanisms have previously been proposed to explain `melt fracture' instabilities that are seen during plastic extrusion, many of which were made on the basis that no linear instability exists. The polymer diffusive instability (PDI) is a recently discovered linear instability that is seen in Oldroyd-B and FENE-P fluids in rectilinear geometries when the effects of polymer stress diffusion are included in the model. We consider PDI in an Oldroyd-B fluid in the concentrated polymer solution limit. We present analytic results, where we identify the boundary layer structure of PDI, and we predict its eigenvalues. We show that PDI could influence the plastic extrusion process due to its large growth rate, and it bears many similarities with the `sharkskin' instability. Inertia is shown to have a destabilising effect, with it lowering the critical Weissenberg number required for the system to become unstable.   

Efficiency loss in viscoelastic turbulent flows due to polymer degradation

Introducing small amounts of long-chain polymers to a viscous liquid has been shown to dramatically reduce skin-friction drag in turbulent flows. One of the main challenges in polymer-induced drag reduction is the mechanical degradation of polymers due to strong elongational strain and shear stresses generated by turbulence. During this process, polymer chains are likely to split, which significantly diminishes drag reduction (DR) effects. For this study, we perform direct numerical simulations of viscoelastic flows using the FENE-P model to investigate the effects of polymer degradation. The simulations are performed at a friction Reynolds number of 100 while other parameters such as Weissenberg number (Wi) and polymer length/concentration are adjusted based on reported experimental observations to model the degradation process. As expected, the degradation contributes to a significant loss of DR effects, where DR% decreases by a factor of at least 3.8 after the first degradation pass. It is also found that the more flexible the polymers (high Wi number), the more loss of DR%. However, there seems to be an apparent saturation reached at sufficiently high Wi numbers. During the second degradation pass, the loss of DR effects becomes less dramatic due to the resulting very low-Wi regime. We will also discuss the effects of the initial polymer length and concentration on the loss of DR effects.   

Vortex ring interaction with a layer of polymeric fluid

Numerical simulations of laminar vortex rings interacting with a layer of polymeric fluid were performed. The results show that when ring-polymer interaction occurs, the flow kinetic energy decreases while enstrophy and dissipation increase. Detailed analysis of the flow reveals that elastic forces act to counter the motion of the ring. Future work will focus on identifying the key non-dimensional parameters, such as the Weissenberg number, that govern this phenomenon.   

Connecting polymer dynamics and Lagrangian flow structures in viscoelastic flows

In viscoelastic flows, the distribution of polymeric stress dictates the onset of elastic instabilities and material transport properties in a wide range of biological and industrial processes. However, measurements of the stress are often non-trivial even in steady flows, due to the intrinsic dependence of the polymer conformation upon the Lagrangian history of fluid deformation. In this work, we employ micro-PIV measurements of viscoelastic flows through a variety of canonical microfluidic geometries to elucidate the link between Lagrangian flow structure and polymer conformation. The measured Lagrangian fluid deformation is directly correlated with real-time imaging of single polymer kinematics in flow across a range of Weissenberg numbers. Our results are additionally compared to the theoretical polymer conformation and to stress fields from numerical simulations. Taken together, this work refines our Lagrangian perspective of viscoelastic flows by illustrating the relationship between fluid stretch and polymeric stress, and has implications for understanding their mixing and transport properties.   

3D measurements of flow topology in a polymer drag-reduced turbulent boundary layer

Three-dimensional particle tracking velocimetry and the invariants of the velocity gradient tensor (VGT), rate of deformation tensor (RDT) and rate of rotation tensor (RRT) are used to characterize the fine scale flow motions in a Newtonian and polymer drag-reduced turbulent boundary layer (TBL). Relative to the Newtonian TBL, the polymer-laden flow has a similar momentum thickness Reynolds number Re_θ of 2300, but a 33% lower skin friction coefficient. Joint probability density functions (JPDFs) of the VGT invariants (Q and R) for the Newtonian TBL produce the familiar tear-drop pattern, commonly seen in direct numerical simulations of Newtonian turbulence. Compared to the Newtonian TBL, the polymer-laden flow has significantly attenuated values of R, implying a reduction in the tendency for the flow to exhibit extension. Invariants in RDT (Q_D and R_D) imply that straining motions within the polymeric flow are more two-dimensional compared to the Newtonian TBL. Moreover, JPDFs of Q_D and the invariant in the RRT (Q_W) suggest that the flow consists of fewer biaxial extensional events and more shear-dominate, sheet-like motions. Few, if any, experimental investigations have measured the fine scale motions in a Newtonian and polymer drag-reduced TBL. This investigation provides the first experimental evidence in support of the notion that an attenuation of biaxial straining motions is central to the mechanism of polymer drag reduction.   

Bubble migration in a viscoelastic duct flow

Interface-resolved direct numerical simulations have been performed to study the bubble migration in a viscoelastic pressure-driven duct flow using the Giesekus model. Flow parameters are varied to reveal the effects of bubble deformability, fluid elasticity, shear thinning and inertia on the bubble migration. The rate of bubble migration is found to be much higher than a solid particle mainly due to the slip condition. The bubble-induced secondary flow velocity is also found to be an order of magnitude higher than the one induced by a solid particle under similar flow conditions. At a higher Weissenberg number, the flow becomes elastically unstable due to the curvature of streamlines across the bubble. It is found that at the lower values of β (polymeric to solvent viscosity ratio), shear thinning effect suppresses this path instability whereas at the higher value of β, shear thinning effect reverses its role and promotes path instability. During the flow build up, the fluctuations are only observed in the migration velocity of the bubble when the dominant lift force is due to elasticity. Simulations are also performed to investigate onset of a chaotic flow by injecting multiple bubbles into the viscoelastic duct flow.   

The nature of bubble-induced turbulence in polymeric fluids for Re ~ Ο(1)

Recent experimental evidence on bubble-induced turbulence showed that the k ^-3 scaling of the energy spectra of velocity fluctuations is replaced by a steeper k ^-6.8 scaling when polymeric additives are present at a moderate Reynolds number. In the present study, we investigate the homogeneous bubble swarm rising at a low Reynolds number in the polymeric fluid. Using particle image velocimetry (PIV), the liquid velocity fluctuations are determined from the decaying turbulence behind the bubble swarm. In the case of viscous Newtonian fluids (Re ~ Ο(1)), the energy spectrum depends on the gas volume fraction (i.e. the number of bubbles). The present talk addresses an intriguing question of how elasticity affects the energy spectrum in bubble-induced turbulence at a low Reynolds number.