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Journal ArticleDOI

On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows

10 Sep 2004-Journal of Fluid Mechanics (Cambridge University Press)-Vol. 514, pp 271-280
TL;DR: In this paper, the authors used numerical simulations of turbulent polymer solutions using the FENE-P model to characterize the action of polymers on turbulence in drag-reduced flows and found that polymers are found to store and to release energy to the flow in a well-organized manner.
Abstract: Numerical simulations of turbulent polymer solutions using the FENE-P model are used to characterize the action of polymers on turbulence in drag-reduced flows. The energetics of turbulence is investigated by correlating the work done by polymers on the flow with turbulent structures. Polymers are found to store and to release energy to the flow in a well-organized manner. The storage of energy occurs around near-wall vortices as has been anticipated for a long time. Quite unexpectedly, coherent release of energy is observed in the very near-wall region. Large fluctuations of polymer work are shown to re-energize decaying streamwise velocity fluctuations in high-speed streaks just above the viscous sublayer. These distinct behaviours are used to propose an autonomous regeneration cycle of polymer wall turbulence, in the spirit of Jimenez & Pinelli (1999).
Citations
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Journal ArticleDOI
TL;DR: A review of recent progress in understanding and predicting polymer drag reduction (DR) in turbulent wall-bounded shear flows is provided in this paper, where numerical simulations of viscoelastic turbulent flows and detailed turbulence measurements in flows of dilute polymer solutions using laser-based optical techniques.
Abstract: This article provides a review of recent progress in understanding and predicting polymer drag reduction (DR) in turbulent wall-bounded shear flows. The reduction in turbulent friction losses by the dilute addition of high–molecular weight polymers to flowing liquids has been extensively studied since the phenomenon was first observed over 60 years ago. Although it has long been reasoned that the dynamical interactions between polymers and turbulence are responsible for DR, it was not until recently that progress had been made to begin to elucidate these interactions in detail. These advancements come largely from numerical simulations of viscoelastic turbulent flows and detailed turbulence measurements in flows of dilute polymer solutions using laser-based optical techniques. This review presents a selective overview of the current state of the numerics and experimental techniques and their impact on understanding the mechanics and prediction of polymer DR. It includes a discussion of areas in which our ...

639 citations

Journal ArticleDOI
TL;DR: It is demonstrated here for a model system of such complex fluids that at high shear rates, turbulence is not simply modified as previously believed but is suppressed and replaced by a different type of disordered motion, elasto-inertial turbulence.
Abstract: Turbulence is ubiquitous in nature, yet even for the case of ordinary Newtonian fluids like water, our understanding of this phenomenon is limited Many liquids of practical importance are more complicated (eg, blood, polymer melts, paints), however; they exhibit elastic as well as viscous characteristics, and the relation between stress and strain is nonlinear We demonstrate here for a model system of such complex fluids that at high shear rates, turbulence is not simply modified as previously believed but is suppressed and replaced by a different type of disordered motion, elasto-inertial turbulence Elasto-inertial turbulence is found to occur at much lower Reynolds numbers than Newtonian turbulence, and the dynamical properties differ significantly The friction scaling observed coincides with the so-called “maximum drag reduction” asymptote, which is exhibited by a wide range of viscoelastic fluids

201 citations


Cites background from "On the coherent drag-reducing and t..."

  • ...The existing theories of drag reduction all share the same conceptual feature: They interpret the resulting flow as a modified form of ordinary Newtonian shear flow turbulence, with its properties being determined by the balance between elastic and viscous stresses (11, 15, 16, 30, 31)....

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Journal ArticleDOI
TL;DR: In this paper, the authors describe simulations of turbulent minimal channel flow of Newtonian fluids and viscoelastic polymer solutions and show that there are intervals of hibernating turbulence that display very low drag as well as many other features of the maximum drag reduction observed in polymer solutions.
Abstract: Addition of a small amount of very large polymer molecules or micelle-forming surfactants to a liquid can dramatically reduce the energy dissipation it exhibits in the turbulent flow regime. This rheological drag reduction phenomenon is widely used, for example, in the Alaska pipeline, but it is not well-understood, and no comparable technology exists to reduce turbulent energy consumption in flows of gases, in which polymers or surfactants cannot be dissolved. The most striking feature of this phenomenon is the existence of a so-called maximum drag reduction (MDR) asymptote: for a given geometry and driving force, there is a maximum level of drag reduction that can be achieved through addition of polymers. Changing the concentration, molecular weight or even the chemical structure of the additives has little to no effect on this asymptotic value. This universality is the major puzzle of drag reduction. We describe direct numerical simulations of turbulent minimal channel flow of Newtonian fluids and viscoelasticpolymer solutions. Even in the absence of polymers, we show that there are intervals of “hibernating” turbulence that display very low drag as well as many other features of the MDR asymptote observed in polymer solutions. As Weissenberg number increases to moderate values the frequency of these intervals also increases, and a simple theory captures key features of the intermittent dynamics observed in the simulations. At higher Weissenberg number, these intervals are altered – for example, their duration becomes substantially longer and the instantaneous Reynolds shear stress during them becomes very small. Additionally, simulations of “edge states,” dynamical trajectories that lie on the boundary between turbulent and laminar flow, display characteristics that are similar to those of hibernating turbulence and thus to the MDR asymptote, again even in the absence of polymer additives. Based on these observations, we propose a tentative unified description of rheological drag reduction. The existence of MDR-like intervals even in the absence of additives sheds light on the observed universality of MDR and may ultimately lead to new flow control approaches for improving energy efficiency in a wide range of processes.

143 citations

Journal ArticleDOI
TL;DR: In this paper, the authors report on the pronounced turbulence modulations and the accompanying drag reduction observed in a two-way coupled simulation of particle-laden channel flow and support the view that drag reduction can be achieved not only by means of polymeric or fiber additives but also with spherical particles.
Abstract: This letter reports on the pronounced turbulence modulations and the accompanying drag reduction observed in a two-way coupled simulation of particle-laden channel flow. The present results support the view that drag reduction can be achieved not only by means of polymeric or fiber additives but also with spherical particles.

141 citations

Journal ArticleDOI
TL;DR: Elasto-inertial turbulence 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.
Abstract: 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 Qa 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 Qa 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 (Wi, ratio polymer relaxation time to viscous time scale). For supercritical Reynolds numbers, flows approach EIT at large Wi. 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.

138 citations

References
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Journal ArticleDOI
TL;DR: In this article, the authors performed direct numerical simulations of unsteady channel flow at low to moderate Reynolds numbers on computational boxes chosen small enough so that the flow consists of a doubly periodic array of identical structures.
Abstract: Direct numerical simulations of unsteady channel flow were performed at low to moderate Reynolds numbers on computational boxes chosen small enough so that the flow consists of a doubly periodic (in x and z) array of identical structures. The goal is to isolate the basic flow unit, to study its morphology and dynamics, and to evaluate its contribution to turbulence in fully developed channels. For boxes wider than approximately 100 wall units in the spanwise direction, the flow is turbulent and the low-order turbulence statistics are in good agreement with experiments in the near-wall region. For a narrow range of widths below that threshold, the flow near only one wall remains turbulent, but its statistics are still in fairly good agreement with experimental data when scaled with the local wall stress. For narrower boxes only laminar solutions are found. In all cases, the elementary box contains a single low-velocity streak, consisting of a longitudinal strip on which a thin layer of spanwise vorticity is lifted away from the wall. A fundamental period of intermittency for the regeneration of turbulence is identified, and that process is observed to consist of the wrapping of the wall-layer vorticity around a single inclined longitudinal vortex.

1,097 citations


"On the coherent drag-reducing and t..." refers result in this paper

  • ...Nevertheless, the turbulence was found to be self-sustained in a similar fashion to the minimal channel flow of Jiménez & Moin (1991) which contains only a pair of streaks and vortices....

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Journal ArticleDOI
TL;DR: In this article, it is shown that a cycle exists which is local to the near-wall region and does not depend on the outer flow, and that the presence of the wall seems to be only necessary to maintain the mean shear.
Abstract: Numerical experiments on modified turbulent channels at moderate Reynolds numbers are used to differentiate between several possible regeneration cycles for the turbulent fluctuations in wall-bounded flows. It is shown that a cycle exists which is local to the near-wall region and does not depend on the outer flow. It involves the formation of velocity streaks from the advection of the mean profile by streamwise vortices, and the generation of the vortices from the instability of the streaks. Interrupting any of those processes leads to laminarization. The presence of the wall seems to be only necessary to maintain the mean shear. The generation of secondary vorticity at the wall is shown to be of little importance in turbulence generation under natural circumstances. Inhibiting its production increases turbulence intensity and drag.

867 citations


"On the coherent drag-reducing and t..." refers background or methods in this paper

  • ...Based on these results, we propose to include the effects of polymers in the autonomous regeneration cycle put forward by Jiménez & Pinelli (1999)....

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  • ...These distinct behaviours are used to propose an autonomous regeneration cycle of polymer wall turbulence, in the spirit of Jiménez & Pinelli (1999)....

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  • ...The numerical method is essentially that of Min et al. (2003b) modified to simulate very elastic and long polymer molecules and is described and validated in Dubief et al....

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  • ...Finally, a model of drag-reduced near-wall turbulence is proposed based on the autonomous regeneration cycle of near-wall turbulence of Jiménez & Pinelli (1999)....

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Journal ArticleDOI
TL;DR: In this paper, it was shown that the pressure Laplacian is positive within a low-pressure tube of small cross section enclosed by convex isobaric surfaces in a uniform density flow.
Abstract: The identification issue of coherent vortices is investigated on the basis of direct numerical simulation (DNS) and large-eddy simulations (LES) of turbulent flows. It is first shown that the pressure Laplacian is positive within a low-pressure tube of small cross section enclosed by convex isobaric surfaces in a uniform-density flow. Since this quantity is related to the second invariant Q of ∇ u , the Q criterion (region where Q is positive) is a necessary condition for the existence of such tubes. This eduction scheme is compared to other classical methods in incompressible simulations of isotropic turbulence: a mixing layer, a channel flow and a backward-facing step. Q-isosurfaces turn out to display very nice coherent vortices. This criterion is also used in combination with a conditional sampling method to discuss the characteristics of quasi-longitudinal vortices in a manipulated channel flow. The contribution of near-wall vortical structures to velocity and vorticity fluctuations is clearly isolat...

797 citations


"On the coherent drag-reducing and t..." refers background or methods in this paper

  • ...These structures are the quasi-streamwise vortices which occupy less than 10% of the volume of the buffer layer (Dubief & Delcayre 2000), yet they are essential to momentum exchanges between outer and inner regions in the flow and are responsible for turbulent skin friction drag (Kravchenko et al.…...

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  • ...in drag-reduced flows has been established by simple numerical experiments reported in Dubief et al. (2004). Based on these results, we propose to include the effects of polymers in the autonomous regeneration cycle put forward by Jiménez & Pinelli (1999). This cycle, shown in figure 5, explains how wall turbulence is self-sustained through mean shear, nonlinear interactions, near-wall vortices and streaks, in the Newtonian case. Polymers fit at the centre of this cycle by extracting energy from the vortices and releasing energy in the streaks. The stretching of polymers is governed by the mean shear and nonlinear interactions as shown in Terrapon et al. (2004). This simple mechanism appears to apply to LDR and HDR regimes, and it should apply to any regime where streaks and vortices are present....

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  • ...…wall friction (Kravchenko, Choi & Moin 1993), occupy a volume of about 10% of the buffer region in Newtonian flows and the streamwise vorticity fluctuations they generate in their core and immediate surroundings exceed the standard deviation of ωx by a factor of 2 or more (Dubief & Delcayre 2000)....

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  • ...(2003b) modified to simulate very elastic and long polymer molecules and is described and validated in Dubief et al. (2004). In the present paper only a brief outline of the method is given. The momentum equations are solved on a staggered grid with second-order central finite differences. The divergence of the polymer stress (2.1) and the spatial derivatives of c̃ij are computed using a fourthorder compact scheme and a third-order upwind compact scheme, respectively. Time advancement of (2.1) and (2.2) is performed by the classical semi-implicit secondorder Crank–Nicolson/third-order Runge–Kutta scheme. In the momentum equation, the Newtonian viscous stress is treated implicitly in the wall-normal direction. Equation (2.2) is solved with a new semi-implicit time scheme which ensures that the trace of the c̃ij remains upper bounded (c̃kk <L (2)). A local artificial viscosity (LAD), proposed by Min et al. (2003b), is necessary to ensure the stability of the advection term as well as a lower diffusive effect than a global dissipation as adopted in Dimitropoulos et al....

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  • ...in drag-reduced flows has been established by simple numerical experiments reported in Dubief et al. (2004). Based on these results, we propose to include the effects of polymers in the autonomous regeneration cycle put forward by Jiménez & Pinelli (1999). This cycle, shown in figure 5, explains how wall turbulence is self-sustained through mean shear, nonlinear interactions, near-wall vortices and streaks, in the Newtonian case....

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Journal ArticleDOI
TL;DR: In this paper, the authors argue that the interaction of turbulence with the polymers introduces mean and fluctuating polymer stresses which can create turbulence, and that the effect of turbulence modification depends on the manner by which polymers are introduced into the flow.
Abstract: Measurements of turbulence properties of solutions of polymers have been made over a large range of drag-reduction, in a fully-developed channel flow. At flows close to maximum drag-reduction the Reynolds stresses were approximately zero over the whole cross section of the channel. Added mean polymer stresses were observed in the viscous wall region for small drag-reduction and over the whole cross-section for large drag-reduction. Even though the Reynolds stresses are zero, the velocity profile is not parabolic because of the presence of these mean stresses. We interpret the results by arguing that the interaction of turbulence with the polymers introduces mean and fluctuating polymer stresses which can create turbulence. The observation that the turbulence modification depends on the manner by which the polymers are introduced into the flow supports the notion that the polymers need to form aggregates in order to be effective.

317 citations


"On the coherent drag-reducing and t..." refers background or methods or result in this paper

  • ...In drag-reduced flow, the maximum of u′+ x is higher than or comparable with the DR = 0% case, as found in experiments (Warholic et al. 1999; Ptasinski et al. 2003; White et al. 2004)....

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  • ...At DR =60%, its near-wall contribution to (3.1) has the same magnitude as the Reynolds shear stress, thus showing that polymers have a significant mean effect in the mechanism of HDR flows, as argued by Warholic et al. (1999)....

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  • ...In drag-reduced flows, a stress deficit is observed in the stress balance whose large magnitude at HDR has been interpreted as the necessary input of energy from the polymers to the flow for the sustenance of the asymptotic MDR turbulence (Warholic et al. 1999)....

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  • ...In drag-reduced flow, the maximum of u′+x is higher than or comparable with the DR = 0% case, as found in experiments (Warholic et al. 1999; Ptasinski et al. 2003; White et al. 2004)....

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  • ...As expected from experiments (Warholic et al. 1999), DR = 35% produces a velocity profile whose log region is only shifted upward, while DR = 47% and DR =60% show significant changes in the slope of the log law (figure 1)....

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Journal ArticleDOI
TL;DR: In this article, a simulation of a turbulent channel flow is presented, where the polymers are modelled as elastic dumbbells using the FENE-P model and the simulation results show that at approximately maximum drag reduction the slope of the mean velocity profile is increased compared to the standard logarithmic profile in turbulent wall flows.
Abstract: It is well known that the drag in a turbulent flow of a polymer solution is significantly reduced compared to Newtonian flow. Here we consider this phenomenon by means of a direct numerical simulation of a turbulent channel flow. The polymers are modelled as elastic dumbbells using the FENE-P model. In the computations the polymer model is solved simultaneously with the flow equations, i.e. the polymers are deformed by the flow and in their turn influence the flow structures by exerting a polymer stress. We have studied the results of varying the polymer parameters, such as the maximum extension, the elasticity and the concentration. For the case of highly extensible polymers the results of our simulations are very close to the maximum drag reduction or Virk (1975) asymptote. Our simulation results show that at approximately maximum drag reduction the slope of the mean velocity profile is increased compared to the standard logarithmic profile in turbulent wall flows. For the r.m.s. of the streamwise velocity fluctuations we find initially an increase in magnitude which near maximum drag reduction changes to a decrease. For the velocity fluctuations in the spanwise and wall-normal directions we find a continuous decrease as a function of drag reduction. The Reynolds shear stress is strongly reduced, especially near the wall, and this is compensated by a polymer stress, which at maximum drag reduction amounts to about 40% of the total stress. These results have been compared with LDV experiments of Ptasinski et al. (2001) and the agreement, both qualitatively and quantitatively, is in most cases very good. In addition we have performed an analysis of the turbulent kinetic energy budgets. The main result is a reduction of energy transfer from the streamwise direction, where the production of turbulent kinetic energy takes place, to the other directions. A substantial part of the energy production by the mean flow is transferred directly into elastic energy of the polymers. The turbulent velocity fluctuations also contribute energy to the polymers. The elastic energy of the polymers is subsequently dissipated by polymer relaxation. We have also computed the various contributions to the pressure fluctuations and identified how these change as a function of drag reduction. Finally, we discuss some cross-correlations and various length scales. These simulation results are explained here by two mechanisms. First, as suggested by Lumley (1969) the polymers damp the cross-stream or wall-normal velocity fluctuations and suppress the bursting in the buffer layer. Secondly, the ‘shear sheltering’ mechanism acts to amplify the streamwise fluctuations in the thickened buffer layer, while reducing and decoupling the motions within and above this layer. The expression for the substantial reduction in the wall drag derived by considering the long time scales of the nonlinear fluctuations of this damped shear layer, is shown to be consistent with the experimental data of Virk et al. (1967) and Virk (1975).

257 citations


"On the coherent drag-reducing and t..." refers background or result in this paper

  • ...In drag-reduced flow, the maximum of u′+ x is higher than or comparable with the DR = 0% case, as found in experiments (Warholic et al. 1999; Ptasinski et al. 2003; White et al. 2004)....

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  • ...It contains the damping of near-wall vortices discussed by Dimitropoulos et al. (2001), Stone et al. (2001), Min et al. (2003b) and Ptasinski et al. (2003)....

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  • ...Statistical results reproduce the main features observed experimentally and in other numerical studies (Ptasinski et al. 2003; Min et al. 2003a)....

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  • ...In drag-reduced flow, the maximum of u′+x is higher than or comparable with the DR = 0% case, as found in experiments (Warholic et al. 1999; Ptasinski et al. 2003; White et al. 2004)....

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  • ...At higher drag reductions, larger than about 40%, the flow enters the HDR regime for which the slope of the log-law is dramatically augmented and the Reynolds shear stress is small (Warholic et al. 1999; Ptasinski et al. 2003)....

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