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

Li, Wei; Graham, Michael D.

doi:10.1063/1.2748443

Cited by 51 publications

(72 citation statements)

References 105 publications

(197 reference statements)

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“…3 The relationship between quasi-streamwise vortices and polymer force was comprehensively illustrated for exact coherent states that mirror the basic structure of near-wall turbulence. 4,5 Recent studies on hairpin vortices originating from the near-wall regions confirmed that polymers effectively apply a negative torque to vortices. 6 The drag reduction results from the dramatic damping and reduction in numbers of quasi-streamwise vortices, the very cause of the dramatic increase in skin-friction drag between laminar and turbulent flows.…”

Section: Introductionmentioning

confidence: 99%

On the mechanism of elasto-inertial turbulence

Dubief¹,

Terrapon²,

Soria³

2013

Physics of Fluids

140

187

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Elasto-inertial turbulence (EIT) is a new state of turbulence found in inertial flows with polymer additives. The dynamics of turbulence generated and controlled by such additives is investigated from the perspective of the coupling between polymer dynamics and flow structures. Direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 (based on the bulk and the channel height) are used to study the formation and dynamics of elastic instabilities and their effects on the flow. The flow topology of EIT is found to differ significantly from Newtonian wall-turbulence. Structures identified by positive (rotational flow topology) and negative (extensional/compressional flow topology) second invariant isosurfaces of the velocity gradient are cylindrical and aligned in the spanwise direction. Polymers are significantly stretched in sheet-like regions that extend in the streamwise direction with a small upward tilt. The cylindrical structures emerge from the sheets of high polymer extension, in a mechanism of energy transfer from the fluctuations of the polymer stress work to the turbulent kinetic energy. At subcritical Reynolds numbers, EIT is observed at modest Weissenberg number (, ratio polymer relaxation time to viscous time scale). For supercritical Reynolds numbers, flows approach EIT at large . EIT provides new insights on the nature of the asymptotic state of polymer drag reduction (maximum drag reduction), and explains the phenomenon of early turbulence, or onset of turbulence at lower Reynolds numbers than for Newtonian flows observed in some polymeric flows.

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Section: Introductionmentioning

confidence: 99%

On the mechanism of elasto-inertial turbulence

Dubief¹,

Terrapon²,

Soria³

2013

Physics of Fluids

140

187

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“…Graham and co-workers [13][14][15][16] have extensively studied modifications of the exact coherent state in viscoelastic flows. They suggested that viscoelasticity weakens the streamwise vortices and that the coherent structures can be suppressed entirely if the elastic effects are sufficiently large.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal evolution of hairpin eddies, Reynolds stress, and polymer torque in polymer drag-reduced turbulent channel flows

Kim

Sureshkumar

2013

Phys. Rev. E

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To study the influence of dynamic interactions between turbulent vortical structures and polymer stress on turbulent friction drag reduction, a series of simulations of channel flow is performed. We obtain self-consistent evolution of an initial eddy in the presence of polymer stresses by utilizing the finitely extensible nonlinear elastic-Peterlin (FENE-P) model. The initial eddy is extracted by the conditional averages for the second quadrant event from fully turbulent Newtonian flow, and the initial polymer conformation fields are given by the solutions of the FENE-P model equations corresponding to the mean shear flow in the Newtonian case. At a relatively low Weissenberg number We(τ) (=50), defined as the ratio of the polymer relaxation time to the wall time scale, the generation of new vortices is inhibited by polymer-induced countertorques. Thus fewer vortices are generated in the buffer layer. However, the head of the primary hairpin is unaffected by the polymer stress. At larger We(τ) values (≥100), the hairpin head becomes weaker and vortex autogeneration and Reynolds stress growth are almost entirely suppressed. The temporal evolution of the vortex strength and polymer torque magnitude reveals that polymer extension by the vortical motion results in a polymer torque that increases in magnitude with time until a maximum value is reached over a time scale comparable to the polymer relaxation time. The polymer torque retards the vortical motion and Reynolds stress production, which in turn weakens flow-induced chain extension and torque itself. An analysis of the vortex time scales reveals that with increasing We(τ), vortical motions associated with a broader range of time scales are affected by the polymer stress. This is qualitatively consistent with Lumley's time criterion for the onset of drag reduction.

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“…Indeed, at Wi = 29 the peak value of α yy , which is closely associated with streamwise vortex suppression [12,16,17], drops from about 210 in active turbulence to about 5 during hibernation, a 40-fold reduction. These results suggest that hibernation should be very similar in the Newtonian and viscoelastic cases.…”

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confidence: 99%

Active and Hibernating Turbulence in Minimal Channel Flow of Newtonian and Polymeric Fluids

Graham

2010

Phys. Rev. Lett.

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100

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Turbulent channel flow of drag-reducing polymer solutions is simulated in minimal flow geometries. Even in the Newtonian limit, we find 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. As viscoelasticity increases, the frequency of these intervals also increases, while the intervals themselves are unchanged, leading to flows that increasingly resemble MDR.The energy dissipated in turbulent channel or pipe flow of a liquid can be dramatically reduced by low levels of long-chain polymer additives [1][2][3]. The most striking qualitative feature of this phenomenon is the existence of a so-called maximum drag reduction (MDR) asymptote [1]. For a given flow geometry at a given pressure drop (i.e. at a given Reynolds number Re), there is an asymptotic maximum flow rate that can be achieved through addition of polymers. Changing the concentration, molecular weight or even the chemical structure of the additives has no effect on this asymptotic value. This universality is the major puzzle of drag reduction.Turbulent flow in or near the MDR regime displays important differences from Newtonian turbulence. Its most commonly discussed signature is a distinctive mean velocity profile U mean (y) that displays clear log-law behavior well-approximated by a formula given by Virk: U + mean = 11.7 ln y + − 17.0 [1] (Superscript "+" denotes quantities nondimensionalized in inner velocity and length scales τ w /ρ and η/ √ ρτ w ; τ w is the time-and area averaged wall shear stress, η and ρ are fluid viscosity and density and y is distance from the wall.) Additionally, streamwise vortices, which dominate near-wall dynamics in Newtonian turbulence, are significantly weakened at MDR. Low-speed streaks become much less wavy in the streamwise direction and the streak spacing is substantially larger [4][5][6][7]. In addition, the Reynolds shear stress near MDR is substantially smaller than in Newtonian turbulence [8][9][10][11]. Indeed, the smallness of Reynolds shear stress is a central issue in a recent phenomenological model of MDR [12]. Based on these observations, many researchers have suggested that turbulence in the MDR regime is "transitional" [3] or "marginal" [12] in some sense that is not yet well-defined, and that the spatiotemporal flow structures that sustain turbulence in this regime are substantially different from those of normal Newtonian turbulence. In the latter case, one simulation approach that has been fruitful in identifying the self-sustaining structures is the so-called minimal flow unit (MFU) approach [13,14]. This approach identifies the smallest flow domain (at a given Reynolds number) in which turbulence can be sustained. Accordingly, temporally intermittent phenomena can be identified more readily than in a large box, where spatial averages incorporate different regions in ...

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

Cited by 51 publications

References 105 publications

On the mechanism of elasto-inertial turbulence

On the mechanism of elasto-inertial turbulence

Spatiotemporal evolution of hairpin eddies, Reynolds stress, and polymer torque in polymer drag-reduced turbulent channel flows

Active and Hibernating Turbulence in Minimal Channel Flow of Newtonian and Polymeric Fluids

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