Time‐series and extended Karhunen–Loève analysis of turbulent drag reduction in polymer solutions

Wang, Sung-Ning; Graham, Michael D.; Hahn, Friedemann; Li, Xi

doi:10.1002/aic.14328

Cited by 36 publications

(32 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These sheets of polymer conformation are accompanied by cylindrical spanwise structures of rotational and extensional flow (Dubief, Terrapon & Soria 2013;Terrapon, Dubief & Soria 2014). Wang et al (2014) affirmed the importance of spanwise independent structures in polymeric turbulent flows, and hinted at a connection between the elasto-inertial turbulence and MDR. By applying proper orthogonal decomposition to time series of both velocity and polymer stress fields from simulations of MDR in minimal flow domains, they demonstrated that the dominant modes in the hibernating state also exhibit a sheet-like structure, with large polymer stretch occurring in thin, isolated layers.…”

Section: Polymeric Turbulent Flowsmentioning

confidence: 92%

“…At long time, the region of positive stretch remains despite the decay of energy and enstrophy. The stretching is isolated in a very narrow region, and is reminiscent of flow structures observed in nonlinear simulations of inertial polymer flows Agarwal et al 2014;Wang et al 2014). The mechanism behind the flow localization can be explained by contracting the polymer conformation (2.6c) to obtain the evolution of c ii , d dt…”

Section: Finite Extensibilitymentioning

confidence: 96%

See 1 more Smart Citation

The dynamics of spanwise vorticity perturbations in homogeneous viscoelastic shear flow

Page

Zaki

2015

J. Fluid Mech.

View full text Add to dashboard Cite

The viscoelastic analogue to the Newtonian Orr amplification mechanism is examined using linear theory. A weak, two-dimensional Gaussian vortex is superposed onto a uniform viscoelastic shear flow. Whilst in the Newtonian solution the spanwise vorticity perturbations are simply advected, the viscoelastic behaviour is markedly different. When the polymer relaxation rate is much slower than the rate of deformation by the shear, the vortex splits into a new pair of co-rotating but counter-propagating vortices. Furthermore, the disturbance exhibits a significant amplification in its spanwise vorticity as it is tilted forward by the shear. Asymptotic solutions for an Oldroyd-B fluid in the limits of high and low elasticity isolate and explain these two effects. The splitting of the vortex is a manifestation of vorticity wave propagation along the tensioned mean-flow streamlines, while the spanwise vorticity growth is driven by the amplification of a polymer torque perturbation. The analysis explicitly demonstrates that the polymer torque amplifies as the disturbance becomes aligned with the shear. This behaviour is opposite to the Orr mechanism for energy amplification in Newtonian flows, and is therefore labelled a 'reverse-Orr' mechanism. Numerical evaluations of vortex evolutions using the more realistic FENE-P model, which takes into account the finite extensibility of the polymer chains, show the same qualitative behaviour. However, a new form of stress perturbation is established in regions where the polymer is significantly stretched, and results in an earlier onset of decay.

show abstract

Section: Polymeric Turbulent Flowsmentioning

confidence: 92%

Section: Finite Extensibilitymentioning

confidence: 96%

The dynamics of spanwise vorticity perturbations in homogeneous viscoelastic shear flow

Page

Zaki

2015

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…Outcome (iii) is critical for the understanding of polymer drag reduction and specifically MDR. Previous studies have concluded that the nature of MDR is Newtonian [23,29,30,37,38] for the same marginally critical Reynolds number. However, the present results suggest that their conclusion is biased by the use of numerical methods that dissipate the small-scale dynamics critical to EIT.…”

Section: Discussionmentioning

confidence: 99%

“…To further demonstrate outcome (ii), the present results can be compared to those of Wang et al [37], who used the same Reynolds number, other polymer parameters and a Schmidt number Sc = 0.5. They reported intermediate drag reduction at Wi τ = 40 and MDR at Wi τ = 100, yet with flow structures that are clearly of Newtonian nature.…”

Section: Discussionmentioning

confidence: 99%

Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

2018

View full text Add to dashboard Cite

The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of FENE-P fluid flows are performed in both two-and three-dimensional straight periodic channels. The Reynolds number is set to Reτ = 85 which is sub-critical for two-dimensional flows but beyond transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions and two moderate Weissenberg numbers, Wiτ = 40, 100, are considered. The simulation results show that sustained turbulence can be observed in two-dimensional sub-critical flows, confirming the existence of a bi-dimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures co-exist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of the typical Newtonian near-wall vortices and (ii) strong similarities between two-and three-dimensional flows when considering larger Wi numbers. The role of the small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed turbulence, eventually leading to the flow laminarization. A sufficiently high Schmidt number (weakly diffusive polymers) is necessary to allow self-sustained turbulence to settle. Although EIT can withstand a low amount of diffusion and remains in a non-laminar chaotic state, adding a finite amount of GAD in the system can have an impact on the dynamics and lead to important quantitative changes, even for Schmidt numbers as large as 10 2 . * vincent.terrapon@ulg.ac.be arXiv:1710.01199v1 [physics.flu-dyn] 3 Oct 2017 2

show abstract

“…The gravity-driven method [46], two counter-rotating bladed disks systems [47], and a Taylor-Couette device [48] have also been used for measuring DR. In addition, direct numerical simulations and statistical analysis techniques are used to study the drag-reducing effect of polymer additives on turbulent channel flow in minimal domains [49,50]. Furthermore, one of the big advantages of this rotating disk flow is that the mixing time of the polymer with the flow can be estimated as the turnover time of the largest eddies which is always less than the 0.2 s injection time.…”

Section: Rotating Disk Flowmentioning

confidence: 99%

Turbulent Drag Reduction with Polymers in Rotating Disk Flow

2015

View full text Add to dashboard Cite

Abstract:The frictional drag in turbulent flow can be drastically reduced by the addition of minute amounts of suitable linear flexible high-molecular-weight polymers, and the various physical characteristics of the polymers used are known to be closely related to the drag reduction efficiency. This feature article briefly reviews polymer additives and factors in the system affecting turbulent drag reduction in external flow, more specifically in a rotating disk flow.

show abstract

Time‐series and extended Karhunen–Loève analysis of turbulent drag reduction in polymer solutions

Cited by 36 publications

References 61 publications

The dynamics of spanwise vorticity perturbations in homogeneous viscoelastic shear flow

The dynamics of spanwise vorticity perturbations in homogeneous viscoelastic shear flow

Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

Turbulent Drag Reduction with Polymers in Rotating Disk Flow

Contact Info

Product

Resources

About