Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session D1: Non-Newtonian Flows: Instability and Turbulence |
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Chair: Alexander Morozov, University of Edinburgh Room: 3000 |
Sunday, November 23, 2014 2:15PM - 2:28PM |
D1.00001: ABSTRACT WITHDRAWN |
Sunday, November 23, 2014 2:28PM - 2:41PM |
D1.00002: Viscoelastic Taylor-Couette instability as an anolog of Magnetorotational instability Innocent Mutabazi, Yang Bai, Olivier Crumeyrolle Our investigation of the viscoelastic instability (VEI) in the corotating Couette-Taylor system is motivated by the prediction of Ogilvie et. al that such an instability is analogous to the MRI (magneto-rotational instability) which is believed to play a key role in the angular momentum transport in accretion disks. This analogy is supported by stretched spring argument developed by Balbus and Hawley which is similar to that of the polymer stretching model in viscoelastic solutions. To our best knowledge, only one experiment by Boldyrev et al. has been reported for the search of the analogy VEI-MRI. We present both theoretical and experimental results obtained in the viscoelastic Couette-Taylor system when both the cylinders are constrained to rotate along the Keplerian and anti-Keplerian lines. The polymer solutions have a constant solution with respect to shear rate and can be described by the Odlroyd-B model. The control parameters are the aspect ratio $\Gamma$, the radius ratio $\eta$, the Reynolds number $Re$, the elastic number $E=Wi/Re$ and the viscosity ratio $S=\mu_p/\mu$. After linear stability analysis, critical modes are oscillatory and non-axisymmetric. The observed modes are either stationary or oscillatory modes. A state diagram allows for a comparison to MRI [Preview Abstract] |
Sunday, November 23, 2014 2:41PM - 2:54PM |
D1.00003: Travelling waves and their stability in elasto-inertial plane Poiseuille flow Toby Searle, Alexander Morozov Purely elastic turbulence occurs in polymer solutions and other viscoelastic fluids when the Reynold's number is very small ($Re<1$) and the Weissenberg number is large. Recent numerical modelling and experimental study has revealed another form of turbulence somewhere between that controlled by inertia and that governed by the elasticity of the fluid. Flows in this elasto-inertial regime support coherent structures that are unlike the usual Newtonian ones, and turbulence sets in at a lower Reynold's number. It is thought that these structures are similar to those present in purely elastic turbulence. We use 2 dimensional exact solutions in plane Poiseuille flow of an Oldroyd-B fluid to investigate this elasto-inertial regime. First we find viscoelastic travelling wave solutions via numerical continuation from their Newtonian counterparts. We investigate how these solutions are affected by the addition of the polymeric fluid and perform a linear stability analysis in the spanwise direction. We find that these viscoelastic travelling-wave solutions are in fact unstable to 3 dimensional perturbations, and discuss how these instabilities differ from those found in Newtonian turbulence. [Preview Abstract] |
Sunday, November 23, 2014 2:54PM - 3:07PM |
D1.00004: The Effect Of Viscosity and Non-Newtonian Rheology On Reaction Enhancement Between Two Initially Distant Scalars Farrokh Shoaei, John Crimaldi The effect of viscosity and non-Newtonian (shear-thinning) rheology on mixing and reaction between two initially distant scalars has been investigated using a two-channel planar laser-induced fluorescence technique (2C-PLIF). The scalars are stirred and mixed in the mildly turbulent (Re=2000) wake of a round cylinder. The scalars are released continuously upstream of the cylinder, with a separation that initially impedes the reaction. The ambient flow is pure water, but the scalar solutions include Xanthan gum to alter their rheology. Results indicate that mixing and reaction rates in the low-Damkohler limit between the two scalars plumes increase as the viscosity of the scalars is increased. The study also shows that the dominant contribution of total reaction derives from the scalar covariance associated with instantaneous flow processes, and depends strongly on viscosity and non-Newtonian rheology of the scalars in the domain. The results have broad implications for biological and ecological mixing processes involving now-Newtonian fluids. [Preview Abstract] |
Sunday, November 23, 2014 3:07PM - 3:20PM |
D1.00005: ABSTRACT WITHDRAWN |
Sunday, November 23, 2014 3:20PM - 3:33PM |
D1.00006: Stability of the boundary layer on a rotating disk for power-law fluids Paul Griffiths, Stephen Garrett The stability of the flow due to a rotating disk is considered for shear-thinning fluids that satisfy the power-law relationship. In this case the basic flow is not an exact solution of the Navier-Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary layer can be determined via a similarity solution. An asymptotic analysis is presented in the limit of large Reynolds number. It is shown that the stationary spiral instabilities observed experimentally in the Newtonian case can be described for shear-thinning fluids by a linear stability analysis. Predictions for the wavenumber and wave angle of the disturbances suggest that shear-thinning fluids may have a stabilizing effect on the flow. The hypotheses of the asymptotic study are confirmed via a numerical investigation. The neutral curves are computed using a sixth-order system of linear stability equations which include the effects of streamline curvature, Coriolis force and the non-Newtonian viscosity model. It is found that the neutral curves have two minima; these are associated with the type I (cross-flow) and type II (streamline curvature) modes. Results indicate that an increase in shear-thinning has a stabilizing effect on both the type I and II modes. [Preview Abstract] |
Sunday, November 23, 2014 3:33PM - 3:46PM |
D1.00007: Exact coherent states in purely elastic parallel shear flows Toby Searle, Alexander Morozov Parallel shear flows provide a model system for the understanding of the transition to and structure of incompressible Newtonian turbulence. The turbulent attractor is often thought of as structured by a series of exact solutions to the Navier-Stokes equations, where a turbulent flow ``pinballs'' between these solutions in phase space. The most intuitive mechanism for the appearance of these structures was formulated by F. Waleffe and is known as ``the self-sustaining process.'' A novel form of turbulence has been discovered in polymeric fluids where the Reynold's number is low, $Re < 1$, and the Weissenberg number (characterising the fluid elasticity) is large. Using an analogy with the Newtonian self-sustaining process, we attempt to construct the purely elastic counterpart for plane Couette flow of polymer solutions. By introducing a forcing term to the coupled Navier-Stokes and Oldroyd-B equations, we observe the formation of purely elastic streaks and consider their linear stability. We find that there exists a previously unrecognised purely elastic analogue of the Kelvin-Helmholtz instability that gives rise to the streamwise waviness of Newtonian coherent structures. We discuss how this instability might close the cycle and lead to a sustained purely elastic coherent structure. [Preview Abstract] |
Sunday, November 23, 2014 3:46PM - 3:59PM |
D1.00008: An ``inverse-Orr'' mechanism for spanwise vorticity amplification in viscoelastic fluids Jacob Page, Tamer Zaki The linear dynamics of spanwise vorticity fluctuations in homogeneous shear flow of a viscoelastic fluid are examined. A weak Gaussian vortex is superposed onto the mean shear and its time evolution is computed for Oldroyd-B and FENE-P fluids. Unlike the Newtonian case where the vortex is purely advected, the polymeric flow exhibits intriguing behaviors: (i) At high elasticity, the vortex splits into a co-rotating pair which propagate in opposing horizontal directions. (ii) For weaker elasticities, the vortex splitting takes place at early times but the evolution is dominated by an algebraic amplification of vorticity. Both the splitting and amplification are explained using the linear equations for spanwise vorticity and polymer torque for the Oldroyd-B fluid. The splitting results from the ability of the fluid to support vorticity wave propagation along the tensioned mean-flow streamlines. The spanwise vorticity amplification occurs due to a kinematic mechanism that generates polymer torque. This mechanism is an ``inverse-Orr'' effect where amplification occurs as the disturbance is tilted into the shear. In the case of finite polymer extensibility, similar qualitative features are retained although decay sets in earlier as polymer chains become significantly stretched. [Preview Abstract] |
Sunday, November 23, 2014 3:59PM - 4:12PM |
D1.00009: POD analysis of viscoelastic flow instabilities David Stein, Becca Thomases Elastic instabilities in low Re viscoelastic flows near extensional points have been identified in experiments and simulations and are thought to be related to elastic turbulence. We study an unsteady two dimensional Stokes Oldroyd-B extensional point flow. Beyond a critical Weissenberg number, the system displays complex time-dependent flow patterns. We examine these quasi-periodic states in detail, and use proper orthogonal decomposition (POD) to extract the dominant oscillatory flow features in an effort to understand the elastic instability and the possible transition to elastic turbulence. [Preview Abstract] |
Sunday, November 23, 2014 4:12PM - 4:25PM |
D1.00010: Simulation of elastic and elasto-inertial turbulence in straight channel flows Yves Dubief, Vincent Terrapon, Samir Sid Elastic turbulence (ET, Nature, {\bf 410}, 905-908, 2000) is a chaotic flow state generated and sustained by polymer additives at vanishing Reynolds numbers. It is generally accepted that elastic turbulence occurs when the mean flow streamlines are curved. Elasto-inertial turbulence (EIT, PNAS, {\bf 220} (26), 10557-10562, 2013) is a similar state of turbulence that happens in inertial flows with mean straight flow streamlines at Reynolds numbers for which the flow is laminar in the absence of polymers. A recent experiment (PRL {\bf 110}, 174502, 2013) has shown that ET generated by the insertion of cylinders at the inlet of a low Reynolds number channel flow is sustained downstream of the perturbation. This experiment suggests a possible relation between ET and EIT. Our study will first confirm that sustained ET can be triggered in low-Reynolds number channel flows. ET is shown to exist in two- and three-dimensional simulations for Reynolds numbers of the order of 100 or less. Much like the aforementioned experiment, the initial conditions triggering ET cause the flow streamlines to be curved for a short duration at the beginning of the simulation. Our study will then discuss the similarities and differences between ET and EIT. [Preview Abstract] |
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