Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session MF: Non-Newtonian Flows I |
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Chair: Patrick Underhill, Rensselaer Polytechnic Institute Room: Long Beach Convention Center 103A |
Tuesday, November 23, 2010 8:00AM - 8:13AM |
MF.00001: Hibernating turbulence, edge states and the Virk asymptote in channel flow of Newtonian and polymeric fluids Michael Graham, Li Xi Turbulent channel flow of Newtonian and drag-reducing polymer solutions is studied computationally. Simulations in the minimal channel geometry reveal that, even in the Newtonian limit, there are intervals of ``hibernating'' turbulence that display many features of the universal maximum drag reduction (MDR) asymptote observed in polymer solutions: weak streamwise vortices, nearly nonexistent streamwise variations and a mean velocity gradient that quantitatively matches experiments (i.e. the Virk log-law). As viscoelasticity increases, the frequency of these intervals also increases, while the intervals themselves are unchanged, leading to flows that increasingly resemble MDR. Simulations in larger channel flow domains as well as turbulent boundary layers reveal spatiotemporally localized regions of active and hibernating turbulence, with hibernating turbulence becoming dominant as the level of viscoelasticity (and drag reduction) increases. Simulations of ``edge states'', dynamical trajectories that lie on the basin boundary between turbulent and laminar flow, display characteristics that are similar to those of hibernating turbulence and thus to the Virk asymptote, again even in the Newtonian limit. [Preview Abstract] |
Tuesday, November 23, 2010 8:13AM - 8:26AM |
MF.00002: Turbulent Drag Reduction by Polymers: A Theoretical Study on the Effect of Polymer Concentration Chung Yin Leung, Emily S.C. Ching A recent theory on turbulent drag reduction by polymers in wall-bounded flows, which is based on the balance of momentum and energy, has been developed [I. Procaccia, V.L. L'ov, and R. Benzi, Rev. Mod. Phys. \textbf{80}, 225 (2008)]. In this theory, the effect of the polymers is understood as a position-dependent effective viscosity. Using this theory, we have carried out a study on the effect of polymer concentration for both flexible and rigid polymers. We have calculated the profiles of the mean velocity and the Reynolds stress and investigated how the profiles change with the polymer concentration. We find some interesting relation between the maximum Reynolds stress and the position of the maximum for a large range of concentration. We have also calculated how the friction factor and the percentage of drag reduction vary with concentration. In this talk, we shall discuss our results and also compare them with experimental observations. [Preview Abstract] |
Tuesday, November 23, 2010 8:26AM - 8:39AM |
MF.00003: On the correspondence between polymer-modified turbulence states and transitional states in Newtonian flows Yves Dubief, Christopher White Polymer addition is known to reduce drag in wall-bounded flows up to an asymptotic state called maximum drag reduction (MDR). The definition of MDR is still largely empirical and its uniqueness is a matter of debate. Using direct numerical simulations, a correspondence is first established between MDR and a specific state of transition in boundary layer flow. A model is derived as a function of the flow topology of the transitional Newtonian flow and the FENE-P model. The model is then extended to natural convection where heat transfer reduction (HTR) and augmentation (HTA) are observed as a function of polymer length. Yet, HTR and HTA are topologically equivalent and again correspond to a transitional state of Rayleigh Benard convection flow. This suggests that polymer-modified turbulence may be predictable as a function of the polymer solution's properties and transitional states of the corresponding Newtonian flow. [Preview Abstract] |
Tuesday, November 23, 2010 8:39AM - 8:52AM |
MF.00004: Parallel Large-Scale Computation of an Oldroyd-B Fluid Past a Confined Circular Cylinder in a Rectangular Channel using an Unstructured Finite Volume Method Mehmet Sahin A new stable unstructured finite volume method is presented for parallel large-scale simulation of viscoelastic fluid flows. The numerical method based on side-centered finite volume method where the velocity vector components are defined at the mid-point of each cell face, while the pressure term and the extra stress tensor are defined at element centroids. The present arrangement of the primitive variables leads to a stable numerical scheme and it does not require any \textit{ad-hoc} modifications in order to enhance the pressure-velocity-stress coupling. The log-conformation representation has been implemented in order improve the limiting Weissenberg numbers in the proposed finite volume method. The time stepping algorithm used decouples the calculation of the extra stresses from the evaluation of the velocity and pressure fields by solving a generalised Stokes problem. The present numerical method is verified for the three-dimensional flow of an Oldroyd-B fluid past a confined sphere in a cylindrical tube. Then the method is applied to the three-dimensional flow of an Oldroyd-B fluid past a confined circular cylinder in a rectangular channel. The computed results at relatively high Weissenberg numbers are discussed and compared to those obtained for Newtonian fluids. [Preview Abstract] |
Tuesday, November 23, 2010 8:52AM - 9:05AM |
MF.00005: A viscoelastic drop falling through a viscous fluid Mukherjee Swarnajay, Kausik Sarkar A viscoelastic drop falling through a Newtonian medium is simulated using a front tracking finite difference method. The drop viscoelasticity deforms the drop into an oblate shape. Further increase in viscoelasticity forms a dimple at the rear end of the drop. The dimple is a result of viscoelastic stresses which pulls the drop interface towards the center. The dimple becomes increasingly prominent as Deborah number or the capillary number is increased. An approximate analysis is executed to model the stress development along the axis of symmetry, specifically its increase near the rear end that governs dimple formation. The model also suggests a shift of the maximum of the viscoelastic stresses toward the centre of the drop with increasing Deborah number. For even higher values of Deborah number, the interface cannot balance the viscoelastic stresses and the dimple grows to make the drop unstable. Unstable cases accompany a decrease in velocity because of the formation of a globular shape at the end of the dimple. This results in a sudden increase in the cross-sectional area of the drop and simultaneous decrease in the settling velocity. Finally, we determine the critical Deborah number for transition from stable to unstable cases for varying capillary number. [Preview Abstract] |
Tuesday, November 23, 2010 9:05AM - 9:18AM |
MF.00006: Simulations of high Reynolds number wake transition in the presence of viscoelasticity David Richter, Gianluca Iaccarino, Eric Shaqfeh Using our three dimensional, time dependent finite volume code developed to compute non-Newtonian flows over a large range of Reynolds number ($Re$), we performed simulations of viscoelastic flow past a circular cylinder. Our focus was on elucidating elastic effects on transition to turbulence in the presence of viscoelasticity. The FENE-P constitutive model was used to describe the presence of polymers, and the numerical method employed was such that a large range of rheological parameters (polymer length $L$, dimensionless Weissenberg number ($Wi$), and polymer concentration $\beta$) could be probed. We present a study of the viscoelastic effects on the inertial wake at high $Re$. Simulations were performed at Reynolds numbers of both 300 and 3900, and in each case we witness significant viscoelastic stabilization of structures typically seen in Newtonian flows. At $Re = 300$, the characteristic Newtonian mode A and mode B instabilities can either be weakened or completely suppressed based on the polymer extensibility $L$ - an effect which has been further confirmed with linear stability analysis. Furthermore, at $Re = 3900$, even a small concentration of low extensibility polymers has the ability to stabilize the shear layer (which has transitioned for pure Newtonian flow), and revert the wake structure back to one resembling the mode B instability, a state seen in Newtonian flows at much lower Reynolds numbers. [Preview Abstract] |
Tuesday, November 23, 2010 9:18AM - 9:31AM |
MF.00007: Evolution of vortical structures in Newtonian and viscoelastic turbulent flows Kyoungyoun Kim, Radhakrishna Sureshkumar To study the influence of dynamical interactions between turbulent vortical structures and polymer stress on turbulent friction drag reduction, a series of simulations were performed for channel flow at $Re_{\tau}$=395. The initial eddy extracted by the conditional averages for the Q2 event from fully turbulent Newtonian flow is self-consistently evolved in the presence of polymer stresses by utilizing the FENE-P model (finitely extensible nonlinear elastic-Peterlin). The initial polymer conformation fields are given by the solutions of FENE- P model equations for the Newtonian mean shear. For a relatively low Weissenberg number, defined as the ratio of fluid relxation time to the time scale of viscous diffusion, ($We_{\tau}$=50) the generation of new vortices is inhibited by polymer-induced counter torques, which results in fewer vortices in the buffer layer. However, the head of primary hairpin unaffected by the polymer stress. For larger values of $We_{\tau}$ ($\ge$100), the hairpin head becomes weaker and vortex auto-generation and Reynolds stress growth are almost entirely suppressed. [Preview Abstract] |
Tuesday, November 23, 2010 9:31AM - 9:44AM |
MF.00008: Peristaltic pumping of solid particles immersed in a viscoelastic fluid John Chrispell, Lisa Fauci Peristaltic pumping of fluid is a fundamental method of transport in many biological processes. In some instances, particles of appreciable size are transported along with the fluid, such as ovum transport in the oviduct or kidney stones in the ureter. In some of these biological settings, the fluid may be viscoelastic. In such a case, a nonlinear constitutive equation to describe the evolution of the viscoelastic contribution to the stress tensor must be included in the governing equations. Here we use an immersed boundary framework to study peristaltic transport of a macroscopic solid particle in a viscoelastic fluid governed by a Navier-Stokes/Oldroyd-B model. Numerical simulations of peristaltic pumping as a function of Weissenberg number are presented. We examine the spatial and temporal evolution of the polymer stress field, and also find that the viscoelasticity of the fluid does hamper the overall transport of the particle in the direction of the wave. [Preview Abstract] |
Tuesday, November 23, 2010 9:44AM - 9:57AM |
MF.00009: Examining the coil-stretch transition in flexible polymers Patrick Underhill, Rangarajan Radhakrishnan The behavior of polymer solutions in elongational flow is important in many applications. An especially important property is the dramatic strain rate hardening resulting from the coil-stretch transition. Predictions of the coil-stretch transition and hysteresis have been verified by visualizing single molecules of double-stranded DNA (ds-DNA). The same behavior has not yet been directly observed in single molecule studies of synthetic polymers or more flexible biopolymers such as single-stranded DNA. Current theories of flexible polymers predict these other polymers will behave in a similar way to ds- DNA. However, we have very recently predicted that these other polymers could have dramatically different behavior; the coil- stretch transition can be eliminated under some conditions. For this purpose, we have altered the common bead-spring chain polymer models and simulated their response in flow using Brownian dynamics (BD). This new model we developed allows us to capture the importance of flexibility, entropic elasticity, hydrodynamic interactions, and solvent quality in an accurate and efficient way. This would have not been possible using conventional methods of including excluded volume as a repulsive interaction potential between beads; such a model would require such a large number of beads interacting that it would not be computational tractable. [Preview Abstract] |
Tuesday, November 23, 2010 9:57AM - 10:10AM |
MF.00010: The dynamics of a simple model for a yield stress fluid Yuriko Renardy, Kara Maki A simple model for a yield stress fluid is obtained from Larson's partially extending convection (PEC) strand model by replacing the zero shear stress limit for large shear rates with a non-negative limit (PECR), and augmenting with a Newtonian solvent (PECR-N). The constitutive behavior of PECR-N exhibits the typical non-monotonic shear stress versus shear rate behavior which allows for yielding to occur above a critical value of applied stress. The experimental determination of yield stress can be complicated by extremely slow yielding which may occur for a range of applied stresses. We therefore focus on the case where the elastic time scale is large compared with the viscous time scale and study the evolution of the conformation tensor for parallel shear flow with prescribed shear stress. The resulting dynamical system is solved both numerically and with asymptotic methods to clarify the different types of solution behavior. We find that multiple time scales are responsible for the path to transition from a fast curve, landing on a slow manifold, and escaping to yielded states which are steady or time-periodic. Novel solution types will be discussed. [Preview Abstract] |
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