Grid-generated turbulence in dilute polymer solutions

Friehe, Carl A.; Schwarz, W. H.

doi:10.1017/s0022112070001763

Cited by 33 publications

(21 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(2)) and for the GOY shell model. In the inertial range, both spectra are indistinguishable and show a Kolmogorov-type k −5/3 behavior with an observed slope of −1.67 ± 0.01 (with errors from leastsquare fits), a result consistent with experiments [4,5] of decaying, homogeneous turbulence behind a grid for a dilute polymer solution. However, significant differences show up in the dissipation range: the spectrum for the FENE-P shell model falls much more slowly than its GOY-model counterpart indicating greatly reduced dissipation at large wavenumbers.…”

supporting

confidence: 82%

Drag reduction by polymer additives in decaying turbulence

2005

View full text Add to dashboard Cite

We present results from a systematic numerical study of decaying turbulence in a dilute polymer solution by using a shell-model version of the FENE-P equations. Our study leads to an appealing definition of drag reduction for the case of decaying turbulence. We exhibit several new results, such as the potential-energy spectrum of the polymer, hitherto unobserved features in the temporal evolution of the kinetic-energy spectrum, and characterize intermittency in such systems. We compare our results with the GOY shell model for fluid turbulence.PACS numbers: 47.27.Gs, 83.60.YzThe phenomenon of drag reduction by polymer additives[1], whereby dilute solutions of linear, flexible, high-molecular-weight polymers exhibit frictional resistance to flow much lower than that of the pure solvent, has almost exclusively been studied within the context of statistically steady turbulent flows since the pioneering work of Toms [2]. By contrast, there is an extreme scarcity of results concerning the effects of polymer additives on decaying turbulence [3]. Experimental studies of decaying, homogeneous turbulence behind a grid indicate, for such dilute polymer solutions, a turbulent energy spectrum similar to that found without polymers [4,5]. However, flow visualization via die-injection tracers[5] and particle image velocimetry [6] show an inhibition of small-scale structures in the presence of polymer additives. To the best of our knowledge decaying turbulence in such polymer solutions has not been studied numerically. We initiate such a study here by using a shell model that is well suited to examining the effects of polymer additives in turbulent flows that are homogeneous and in which bounding walls have no direct role. We obtain several interesting results including a natural definition of the percentage dragreduction DR, which has been lacking for the case of decaying turbulence. We show that the dependence of DR on the polymer concentration c is in qualitative accord with experiments[1] as is the suppression of small-scale structures which we quantify by obtaining the filteredwavenumber-dependence of the flatness of the velocity field. We will use a shell-model version of the FENE-P (Finitely Extensible Nonlinear Elastic -Peterlin) [7,8] model for dilute polymer solutions that has often been used for studying viscoelastic effects since it contains the basic characteristics of molecular stretching, orientation and finite extensibility seen in polymer molecules. A direct numerical simulation of the FENE-P equations is computationally prohibitive. This motivates the use of a shell model that captures the essential features of the FENE-P equations. Recent studies [9] have exploited a formal analogy[10] of the FENE-P equations with those of magnetohydrodynamics (MHD) to construct such a shell model. We investigate decaying turbulence in a dilute polymer solution by developing a similar shell model for the FENE-P equations. The unforced FENE-P equations [7,8] arewhere p is the pressure, ν s the kinematic viscosity of the solven...

show abstract

supporting

confidence: 82%

Drag reduction by polymer additives in decaying turbulence

2005

View full text Add to dashboard Cite

show abstract

“…2(b)] that can be explained in terms of a polymer-induced, scale-dependent viscosity. Experiments [16,17] do not resolve the dissipation range as clearly as we do, so the experimental verification of the deep-dissipation-range behavior of Fig. 2(a) remains a challenge.…”

Section: H Y S I C a L R E V I E W L E T T E R S Week Ending 31 Decemmentioning

confidence: 59%

“…However, the existence of drag-reduction-type phenomena in turbulent flows that are homogeneous and isotropic [9][10][11][12][13][14][15][16][17][18][19] remains controversial. Some experimental [15][16][17][18], numerical [11][12][13][14], and theoretical [9,10] studies have suggested that drag reduction should occur even in homogeneous, isotropic turbulence; but other studies have refuted this claim [19].…”

Section: Manifestations Of Drag Reduction By Polymer Additives In Decmentioning

confidence: 99%

Manifestations of Drag Reduction by Polymer Additives in Decaying, Homogeneous, Isotropic Turbulence

2006

View full text Add to dashboard Cite

The existence of drag reduction by polymer additives, well established for wall-bounded turbulent flows, is controversial in homogeneous, isotropic turbulence. To settle this controversy we carry out a high-resolution direct numerical simulation (DNS) of decaying, homogeneous, isotropic turbulence with polymer additives. Our study reveals clear manifestations of drag-reduction-type phenomena: On the addition of polymers to the turbulent fluid we obtain a reduction in the energy dissipation rate, a significant modification of the fluid energy spectrum especially in the deep-dissipation range, a suppression of small-scale intermittency, and a decrease in small-scale vorticity filaments.

show abstract

“…[8][9][10] The nature of the effect of dilute polymers on different turbulent free shear flows has been studied by several authors. There are works [11][12][13][14][15][16] and more recent Ref. 17 that show how in grid turbulence the turbulent kinetic energy decays slower in dilute polymer solutions than in clear water.…”

Section: Introductionmentioning

confidence: 99%

On turbulent entrainment and dissipation in dilute polymer solutions

et al. 2009

View full text Add to dashboard Cite

We present a comparative experimental study of a turbulent flow developing in clear water and dilute polymer solutions ͑25 and 50 wppm polyethylene oxide͒. The flow is forced by a planar grid that oscillates vertically with stroke S and frequency f in a square container of initially still fluid. Two-component velocity fields are measured in a vertical plane passing through the center of the tank by using time resolved particle image velocimetry. After the forcing is initiated, a turbulent layer develops that is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/nonturbulent interface ͑TNTI͒. The turbulent region grows in time through entrainment of surrounding fluid until the fluid in the whole container is in turbulent motion. From the comparison of the experiments in clear water and polymer solutions we conclude: ͑i͒ Polymer additives modify the large scale shape of the TNTI. ͑ii͒ Both, in water and in the polymer solution the mean depth of the turbulent layer, H͑t͒, follows the theoretical prediction for Newtonian fluids H͑t͒ ϰ ͱ Kt, where2 f is the "grid action." ͑iii͒ We find a larger grid action for dilute polymer solutions than for water. As a consequence, the turbulent kinetic energy of the flow increases and the rate of energy input becomes higher. ͑iv͒ The entrainment rate ␤ = v e / v rms ͑where v e = dH / dt is the interface propagation velocity and v rms is the root mean square of the vertical velocity͒ is lower for polymers ͑␤ p Ϸ 0.7͒ than for water ͑␤ w Ϸ 0.8͒. The measured values for ␤ are in good agreement with similarity arguments, from which we estimate that in our experiment about 28% of the input energy is dissipated by polymers.

show abstract

Grid-generated turbulence in dilute polymer solutions

Cited by 33 publications

References 12 publications

Drag reduction by polymer additives in decaying turbulence

Drag reduction by polymer additives in decaying turbulence

Manifestations of Drag Reduction by Polymer Additives in Decaying, Homogeneous, Isotropic Turbulence

On turbulent entrainment and dissipation in dilute polymer solutions

Contact Info

Product

Resources

About