Polymer dynamics in a model of the turbulent buffer layer

Stone, Phillip A.; Graham, Michael D.

doi:10.1063/1.1563258

Cited by 49 publications

(52 citation statements)

References 40 publications

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“…To address this point, we have previously compared FENE-P to more realistic bead-spring-chain models for calculating the stresses in the flow field of a Couette flow ECS. 44 We performed Brownian dynamics simulations of 20-spring chains, with hydrodynamic and excluded volume interactions among the polymer segments explicitly included, as they moved along Lagrangian trajectories in the ECS. Comparing the FENE-P results to the "exact" results from the chain models, we found that the FENE-P model qualitatively captured the spatial variations in polymer stress.…”

Section: Mathematical Formulation and Simulation Detailsmentioning

confidence: 99%

“…(This process of polymer molecules stretching in the streaks and relaxing at the edges of the vortices is also confirmed by Brownian dynamics simulations of model polymers along a Lagrangian trajectory in the ECS. 44 ) The result of this process of stretching and relaxation of the polymer is a region of high polymer stress in the streamwise streak and a region of lower polymer stress where fluid elements have left the streaks and begun to move around one of the vortices. Taking the divergence of the polymer stress gives a force due to the polymer that is directly opposed to the movement of fluid into the vortex.…”

Section: Given Whatmentioning

confidence: 99%

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Polymer drag reduction in exact coherent structures of plane shear flow

et al. 2004

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Recently discovered traveling-wave solutions to the Navier-Stokes equations in plane shear geometries provide model flows for the study of turbulent drag reduction by polymer additives. These solutions, or "exact coherent states" (ECS), qualitatively capture the dominant structure of the near-wall buffer region of shear turbulence, i.e., counter-rotating pairs of streamwise-aligned vortices flanking a low-speed streak in the streamwise velocity. The optimum length scales for the ECS match well the length scales of the turbulent coherent structures and evidence suggests that the ECS underlie the dynamics of these structures. We study here the effect of viscoelasticity on these states. The changes to the velocity field for the viscoelastic ECS, where the FENE-P model calculates the polymer stress, mirror the modifications seen in experiments of fully turbulent flows of polymer solutions at low to moderate levels of drag reduction: drag is reduced, streamwise velocity fluctuations increase while wall-normal fluctuations decrease, and smaller wavelength structures are suppressed. These modifications to the ECS are due to the suppression of the streamwise vortices. The polymer molecules become highly stretched in the wavy, streamwise streaks, where the flow is predominately elongational, then relax as they move from the streaks into and around the streamwise vortices, where the flow is predominately rotational. This relaxation of the polymer molecules produces a force that directly opposes the fluid motion in the vortices, weakening them. Since the pressure fluctuations have their greatest magnitude (i.e., they are most negative) in the cores of the vortices, a reduction in vortex strength leads to a decrease in the magnitude of the pressure fluctuations. The pressure fluctuations redistribute energy from the streamwise velocity fluctuations to the Reynolds shear stress, so a decrease in their magnitude leads to a reduction in turbulent drag. For the viscoelastic ECS, we also find that after the onset of drag reduction (at Weissenberg number, WeϷ 7) there is a dramatic increase in the critical wall-normal length scale at which the ECS can exist. This sharp increase in length scale mirrors experimental observations and is also consistent with the observed shift to higher Reynolds numbers of the transition to turbulence in polymer solutions.

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Section: Mathematical Formulation and Simulation Detailsmentioning

confidence: 99%

Section: Given Whatmentioning

confidence: 99%

Polymer drag reduction in exact coherent structures of plane shear flow

et al. 2004

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“…6). It is tempting to speculate that they are fingerprints of the coherent structures characterizing the flow close to the wall (Nagata 1990;Busse 1992, 1997;Eckhardt 1997, 2000;Eckhardt et al 2002;Stone and Graham 2003) whose relative strength might be influenced by the polymer concentration (De Angelis et al 2003). A further detailed investigation of this phenomenon is necessary.…”

Section: Discussionmentioning

confidence: 99%

Turbulent drag reduction in dam-break flows

et al. 2004

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The role of turbulence is investigated in dambreak flows, where a finite volume of fluid is released from a compartment into a long, rectangular channel. After a sudden removal of the lock gate, a gravity current, undular bore, or solitary wave develops, depending on the ambient fluid height in the channel. The temporal evolution of the moving front has been measured and evaluated. It was observed that the dilution using a very small amount (a few weight ppm) of a long chain polymer (polyethyleneoxide) in the fluid strongly affected flow properties. Pronounced drag reduction has been found in dry bed flows (whereas the polymer increased the viscosity of the fluid). The presence of a few mm-thick ambient fluid layer in the channel effectively destroyed drag reduction, in spite of the fact that strong turbulence was obvious and the propagation velocity of the front was almost unchanged.

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“…It is straightforward to show (see e.g. (Lumley, 1972;Stone and Graham, 2003;Balkovsky et al, 2000Balkovsky et al, , 2001Chertkov, 2000)) that, for a Hookean dumb- …”

Section: Existence Of the Ecsmentioning

confidence: 99%

“…In prior work, our group has studied the initial effects of viscoelasticity on ECS in the plane Couette geometry (Stone et al, 2002;Stone and Graham, 2003;Stone et al, 2004).…”

Section: Introductionmentioning

confidence: 99%

Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow

Graham

2007

Physics of Fluids

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Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. The present work examines the effect of polymer additives on these "exact coherent states" (ECS) in the plane Poiseuille geometry, using the FENE-P constitutive model for polymer solutions. In experiments with a given fluid, Reynolds and Weissenberg numbers are linearly related (i.e. Wi/Re = const).In this situation, we study the effects of viscoelasticity on velocity field and polymer stress field along some experimental paths, which represent different flow behaviors as Re (and Wi) increases. The changes to the velocity field for the viscoelastic nonlinear traveling waves qualitatively capture many of those experimentally observed in fully turbulent flows of polymer solutions at low to moderate levels of drag reduction: drag is reduced, streamwise velocity fluctuations increase, wall-normal and spanwise velocity fluctuations decrease. The mechanism underlying these observations is the suppression of streamwise vortices by the polymer forces exerted on the fluid. Specifically, at sufficiently high wall shear rates, viscoelasticity completely suppress these streamwise vortices in the near-wall region, as is found in experiments in the maximum drag reduction (MDR) regime. The mean shear stress balance for the nonlinear traveling waves show that Reynolds shear stress decreases and polymer stress increases monotonically with the increase of viscoelasticity, as are found in full turbulence. The study of the influence of the viscoelasticity on the turbulent kinetic energy and Reynolds stress budgets shows that as Re (and Wi) increases, there is a consistent decrease in the production, diffusion and dissipation of turbulent kinetic energy. The decrease in the velocity pressure gradient term leads to a redistribution of the turbulent kinetic energy among the streamwise, iii wall-normal and spanwise directions. The influence of the rheological parameters on the viscoelastic ECS is analyzed. It is found that the degree of drag reduction is determined primarily by the extensional viscosity and Weissenberg number. The optimum wavelength conditions under which the viscoelastic ECS first come into existence are also investigated. The wavelengths in streamwise and spanwise directions and the wallnormal extent of the ECS all increase monotonically with the increase of viscoelasticity, as is found in experiments. Examination of the parameter space (Re, Wi) in which ECS exist indicates that at least at the Reynolds number considered here, the transition behaviors from laminar to turbulent flow, from no drag reduction to drag reduction, and from moderate drag reduction to MDR can be connected to the birth, evolution and death of these ECS, respectively.In order to test the scenario that we infer from these results, we next implement direct numerical simulation (DNS), studying the transient and statistical...

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Polymer dynamics in a model of the turbulent buffer layer

Cited by 49 publications

References 40 publications

Polymer drag reduction in exact coherent structures of plane shear flow

Polymer drag reduction in exact coherent structures of plane shear flow

Turbulent drag reduction in dam-break flows

Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow

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