Flow visualization of the near-wall region in a drag-reducing channel flow

Donohue, George; Tiederman, W. G.; Reischman, M. M.

doi:10.1017/s0022112072002514

Cited by 110 publications

(70 citation statements)

References 20 publications

(14 reference statements)

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“…Observations of drag-reducing fluids indicate that, at least near the onset Reynolds number for drag reduction, the effects of the polymer are confined primarily to the near-wall buffer layer, 1,[5][6][7][8] which is the most important region for the production and dissipation of turbulent energy. 9 From experia)…”

Section: Introductionmentioning

confidence: 99%

“…Most notably, the wall-normal thickness of the buffer region increases, 1 the coherent structures in this region shift to larger length scales, 5,[12][13][14] and the bursting rate decreases. 5 These structural changes are accompanied by changes in the root-mean-square (rms) velocity fluctuations and Reynolds stresses. Namely, the wall-normal and spanwise fluctuations are reduced while, at least at low to moderate degrees of drag reduction, the streamwise velocity fluctuations are enhanced.…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Polymer drag reduction in exact coherent structures of plane shear flow

et al. 2004

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“…The changes in the burst events in drag-reducing flows are particularly interesting because the variations of velocity field in the near-wall region during a burst could reveal the mechanism of DR and could also exhibit the basic relationship of turbulent structures. Donohue et al 22 examined the effects of polymers on turbulent structures by using the visualization technique; they reported that the streaking spacing and bursting rates in drag-reducing flow are different from that in the Newtonian flow, i.e., the average nondimensional spacing between streaks linearly increases with increasing DR and the viscous sublayer was more stable when polymer solutions were present. A suppression of the burst process and an increment of streak spacing were also reported by Berman 16 and Tiederman et al 23 However, Luchik and Tiederman 19 found that the method for deducing the time between bursts was not accurate in these experiments because they did not marked and counted all of these events.…”

Section: Introductionmentioning

confidence: 99%

Modeling of viscoelastic turbulent flow in channel and pipe

Yang

Dou

2008

Physics of Fluids

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This paper investigates turbulent flows with or without polymer additives in open channels and pipes. Equations of mean velocity, root mean square of velocity fluctuations, and energy spectrum are derived, in which the shear stress deficit model is used and the non-Newtonian properties are represented by the viscoelasticity ␣ * . The obtained results show that, with ␣ * increment, ͑1͒ the streamwise velocity fluctuations is increased, ͑2͒ the wall-normal velocity fluctuation is attenuated, ͑3͒ the Reynolds stress is reduced, and ͑4͒ there is a redistribution of energy from high frequencies to the low frequencies for the streamwise component, but dimensionless distribution over all frequencies almost remains the same as that in Newtonian fluid flows. Good agreement between the derived equations and experimental data in small drag-reduction regime is achieved, which indicates that the present model is workable for Newtonian/non-Newtonian fluid turbulent flows.

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“…The central rheological feature of drag-reducing additives is their extensional behavior in solution: for dilute polymer solutions in particular the stresses arising in extensional flow can be orders of magnitude larger than those developed in a shear flow. This fact is well-recognized; nevertheless the mechanism of interaction between polymer stretching and turbulent structure is not well-understood and the goal of the present work is to attempt to shed light on this interaction.A key structural observation from experiments and direct numerical simulations (DNS) of drag-reducing solutions is the modification of the buffer region near the wall [4,5,6,7,8,9,10]. It has long been known that the flow in this region is very structured, containing streamwise vortices that lead to streaks in the streamwise velocity [11]; these structures are thickened in both the wall-normal and spanwise directions during flow of drag reducing solutions [4,5].…”

mentioning

confidence: 99%

“…It has long been known that the flow in this region is very structured, containing streamwise vortices that lead to streaks in the streamwise velocity [11]; these structures are thickened in both the wall-normal and spanwise directions during flow of drag reducing solutions [4,5]. Because of its importance in the production and dissipation of turbulent energy [11], any effort to mechanistically understand rheological drag reduction should address this region.…”

mentioning

confidence: 99%

Toward a Structural Understanding of Turbulent Drag Reduction: Nonlinear Coherent States in Viscoelastic Shear Flows

Stone

Waleffe²,

Graham

2002

Phys. Rev. Lett.

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Nontrivial steady flows have recently been found that capture the main structures of the turbulent buffer layer. We study the effects of polymer addition on these "exact coherent states" (ECS) in plane Couette flow. Despite the simplicity of the ECS flows, these effects closely mirror those observed experimentally: structures shift to larger length scales, wall-normal fluctuations are suppressed while streamwise ones are enhanced, and drag is reduced. The mechanism underlying these effects is elucidated. These results suggest that the ECS are closely related to buffer layer turbulence.PACS numbers: 83.60. Yz,83.80.Rs,47.20.Ky,47.27.Cn Rheological drag reduction, the suppression by additives of skin friction in turbulent flow, has received much attention since its discovery in 1947 [1,2,3]. For many polymer-solvent systems, the pressure drop measured in the pipe flow of the solution can be 30 − 50% less than for the solvent alone. The central rheological feature of drag-reducing additives is their extensional behavior in solution: for dilute polymer solutions in particular the stresses arising in extensional flow can be orders of magnitude larger than those developed in a shear flow. This fact is well-recognized; nevertheless the mechanism of interaction between polymer stretching and turbulent structure is not well-understood and the goal of the present work is to attempt to shed light on this interaction.A key structural observation from experiments and direct numerical simulations (DNS) of drag-reducing solutions is the modification of the buffer region near the wall [4,5,6,7,8,9,10]. It has long been known that the flow in this region is very structured, containing streamwise vortices that lead to streaks in the streamwise velocity [11]; these structures are thickened in both the wall-normal and spanwise directions during flow of drag reducing solutions [4,5]. Because of its importance in the production and dissipation of turbulent energy [11], any effort to mechanistically understand rheological drag reduction should address this region.To better understand the effect of the polymer on the buffer layer, we wish to study a model flow that has structures similar to those seen in this region but without the full complexities of time-dependent turbulent flows. Fortunately, a family of such flows exists, in the recently-discovered "exact coherent states" (ECS) found by computational bifurcation analysis in plane Couette and plane Poiseuille flows [12,13,14,15,16]. These are three-dimensional, traveling wave flows (hence steady in a traveling reference frame) that appear via saddle-node bifurcations [35] at a Reynolds number somewhat below the transition value seen in experiments [17,18]. The structure of the ECS captures the counter-rotating staggered streamwise vortices that dominate the structure in the buffer region. From the dynamical point of view, there is evidence that these states form a part of the dynamical skeleton of the turbulent flow: i.e., they are saddle points that underlie the strange attract...

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Flow visualization of the near-wall region in a drag-reducing channel flow

Cited by 110 publications

References 20 publications

Polymer drag reduction in exact coherent structures of plane shear flow

Polymer drag reduction in exact coherent structures of plane shear flow

Modeling of viscoelastic turbulent flow in channel and pipe

Toward a Structural Understanding of Turbulent Drag Reduction: Nonlinear Coherent States in Viscoelastic Shear Flows

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