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 ...

Mechanics and Prediction of Turbulent Drag Reduction with Polymer Additives

In this work, we present from first principles a direct numerical simulation (DNS) of a fully turbulent channel flow of a dilute polymer solution. The polymer chains are modeled as finitely extensible and elastic dumbbells. The simulation algorithm is based on a semi-implicit, time-splitting technique which uses spectral approximations in the spatial coordinates. The computations are carried out on a CRAY T3D parallel computer. The simulations are carried out under fully turbulent conditions albeit, due to computational constraints, not at as high Reynolds number as that usually encountered in polymer-induced drag reduction experiments. In order to compensate for the lower Reynolds number, we simulate more elastic fluids than the ones encountered in drag reduction experiments resulting in Weissenberg numbers (a dimensionless number characterizing the flow elasticity) of similar magnitude. The simulations show that the polymer induces several changes in the turbulent flow characteristics, all of them consi...

Direct numerical simulation of the turbulent channel flow of a polymer solution

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).

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Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms

Drag reduction due to dilute addition of high polymers has been known for about fifty years. In spite of this long history, many aspects of the problem remain poorly understood. Two of its features for pipe flow are considered here in the context of the elastic theory of de Gennes: the onset of drag reduction and the so-called maximum drag reduction (MDR) asymptote. A cautious conclusion is that a version of the theory agrees qualitatively with existing experiments.

The onset of drag reduction by dilute polymer additives, and the maximum drag reduction asymptote

In this work, we present the results from direct numerical simulations of the fully turbulent channel flow of a polymer solution. Using constitutive equations derived from kinetic and network theories, in particular the FEN E-P and the Giesekus models, we predict drag reduction for a variety of rheological parameters, extending substantially previous calculations, [Sureshkumar et al., Phys. Fluids, 9 (1997) 743-755]. The simulation algorithm is based on a semi-implicit, time-splitting technique which uses spectral approximations in the spatial domain. The computations were carried out on a CRAY T3E-900 parallel supercomputer, under fully turbulent conditions. In this work, we demonstrate the existence of a critical range of the Weissenberg number, where the onset of drag reduction occurs, which is independent of the model and also remains the same as the chain extensibility is increased. By allowing for higher extensibility of the polymer chains, we also observed an almost triple in magnitude increase in drag reduction from previous and reported results. The simulations show that the polymer induces several changes in the turbulent flow characteristics, all of them consistent with available experimental results. In addition to decreased fluctuations in the streamwise vorticity and increased streak spacing, we have seen changes, such as the increase of the slope of the logarithmic layer asymptote for the mean velocity profile, which are consistent with high magnitude of drag reduction, as well as with the behaviour of more concentrated systems. This is more consistent with the use of the Giesekus model, which is well suited for concentrated systems, suggesting that there is potential with that model for capturing quite subtle changes in the structure of the turbulent flow field. Results for different contributions of molecular extensibility, L, and solvent viscosity ratio, β, indicate that for the FENE-P model the phenomena are determined almost exclusively by the extensional viscosity and Weissenberg number. However, results obtained with the Giesekus model, for the same extensional viscosity, demonstrate a further drag reducing effect which can be attributed to the non-zero second normal stress coefficient. All results point to a mechanism for drag reduction where a partial inhibition of eddies within the buffer layer by the macromolecules. The simulation results are consistent with the hypothesis that one of the prerequisites for the phenomenon of drag reduction is sufficiently enhanced extensional viscosity, corresponding to the level of intensity and duration of extensional rates typically encountered during the turbulent flow, as has been proposed by various investigators in the past.

Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: effect of the variation of rheological parameters

Aqueous solutions of drag-reducing polymers were injected into turbulent water flow in a pipe. The injection point was situated where the flow was well-developed. Thus, subsequent streamwise variations in pressure drop were due to the injected polymer spreading out across the pipe. The axial development of local drag reduction was monitored by a series of closely-spaced pressure tappings. The corresponding radial dispersion of the injected polymer, as it travelled downstream, was assessed by sampling the flow at various points. Local drag reduction, due to either point injection at the centerline or injection through a slot in the wall, was found to increase with distance downstream. This increase was related to the streamline increase of polymer concentration in a narrow annulus near the pipe wall. It was tentatively concluded that the effective annulus was bounded by 15 less than or equal to y + greater than or equal to 100, in agreement with previous deductions from less direct evidence.

Local drag reduction due to injection of polymer solutions into turbulent flow in a pipe. Part I: Dependence on local polymer concentration

Aqueous solutions of polyethyleneoxide (Polyox WSR-301) were injected into a pipe flow through either a small tube at the center line or an annular slot in the wall. The solution contained polymer at an injection concentration of 1,000 wppm. Injection into water flow with a Reynolds number Re = 3.5 X 10/sup 4/ was at a rate which gave a mean polymer concentration of 5.0 wppm in the water flow. A laser-Doppler anemometer (LDA) was used to measure the streamwise turbulent velocity at various radial positions and at several stations downstream from the injection point. Results were obtained for mean velocity and intensity profiles; autocorrelations; and one-dimensional energy spectra. The mean bursting period was determined using the ''short-sampling-time'' autocorrelation method. Changes in all these quantities due to polymer injection were found to depend on the amount of local drag reduction at that particular downstream station but were independent of the local polymer concentration at the measuring point.

Local drag reduction due to injection of polymer solutions into turbulent flow in a pipe. Part II: Laser‐doppler measurements of turbulent structure

Turbulent drag reduction produced by injection of polymer at the centerline of a pipe flow was found to increase with streamwise distance from the injection point. This was due to radial dispersion of the injected polymer. A tentative relationship between the two is proposed.

Development of local turbulent drag reduction due to nonuniform polymer concentration

Heat Transfer of Non-Newtonian Drag Reducing Flow in Porous Media

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L. H. Rabie

Papers

Local drag reduction due to injection of polymer solutions into turbulent flow in a pipe. Part I: Dependence on local polymer concentration

Local drag reduction due to injection of polymer solutions into turbulent flow in a pipe. Part II: Laser‐doppler measurements of turbulent structure

Development of local turbulent drag reduction due to nonuniform polymer concentration

Heat Transfer of Non-Newtonian Drag Reducing Flow in Porous Media

Non- Newtonian Drag Reducing Flow Characteristics in Porous Media