Large is different: Nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers

Rosti, Marco E.; Perlekar, Prasad; Mitra, Dhrubaditya

doi:10.1126/sciadv.add3831

Cited by 12 publications

(23 citation statements)

References 66 publications

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“…The power-law behaviour of the p.d.f. of has been confirmed in various flow configurations: experimentally by direct observation of individual polymers in elastic turbulence (Gerashchenko, Chevallard & Steinberg 2005; Liu & Steinberg 2010, 2014); and numerically in shear turbulence (Eckhardt, Kronjäger & Schumacher 2002; Puliafito & Turitsyn 2005), in two- and three-dimensional isotropic turbulence (Boffetta, Celani & Musacchio 2003; Watanabe & Gotoh 2010; Gupta, Perlekar & Pandit 2015; Rosti, Perlekar & Mitra 2023), and in turbulent channel and pipe flows (Bagheri et al. 2012; Serafini et al.…”

Section: Introductionmentioning

confidence: 84%

“…In fact, at large values of , this effect can be strong enough to cause the mean extension to decrease with increasing (Rosti et al. 2023). But what if one compensates for the reduced mean value by suitable rescaling?…”

Section: Discussionmentioning

confidence: 99%

“…2016; Valente, da Silva & Pinho 2016; Rosti et al. 2023) and experimental (Vonlanthen & Monkewitz 2013; Zhang et al. 2021).…”

Section: Stationary Statistics Of Polymer Stretchingmentioning

confidence: 99%

“…2021; Rosti et al. 2023) – the velocity structure functions scale anomalously – but the high-order structure functions of the polymer extension field have not been investigated yet. Future work in this direction would be helpful in understanding how extreme events arise and co-evolve in the face of strong fluid–polymer coupling.…”

Section: Stationary Statistics Of Polymer Stretchingmentioning

confidence: 99%

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Polymers in turbulence: stretching statistics and the role of extreme strain rate fluctuations

Picardo,

Plan,

Vincenzi

2023

J. Fluid Mech.

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Polymers in a turbulent flow are stretched out by the fluctuating velocity gradient and exhibit a broad distribution of extensions $R$ ; the stationary probability density function (p.d.f.) of $R$ has a power-law tail with an exponent that increases with the Weissenberg number $\mathit {Wi}$ , a non-dimensional measure of polymer elasticity. This study addresses the following questions. (i) What is the role of the non-Gaussian statistics of the turbulent velocity gradient on polymer stretching? (ii) How does the p.d.f. of $R$ evolve to its asymptotic stationary form? Our analysis is based on simulations of the dynamics of finitely extensible bead–spring dumbbells and chains, in the extremely dilute limit, that are transported in a homogeneous and isotropic turbulent flow, as well as in a Gaussian random flow. We show that while the turbulent flow is more effective at stretching small- $\mathit {Wi}$ stiff polymers, the Gaussian flow is more effective for high- $\mathit {Wi}$ polymers. This suggests that high- $\mathit {Wi}$ polymers (with large relaxation times) are stretched primarily by the cumulative effect of moderate strain rate events, rather than by short-lived extreme-valued strain rates. Next, we show that, beginning from a distribution of coiled polymers, the p.d.f. of $R$ exhibits two distinct regimes of evolution. At low to moderate $\mathit {Wi}$ , the p.d.f. quickly develops a power-law tail with an exponent that evolves in time and approaches its stationary value exponentially. At high $\mathit {Wi}$ , the rapid stretching of polymers first produces a peak in the p.d.f. near their maximum extension; a power law with a constant exponent then emerges and expands its range towards smaller $R$ . The time scales of equilibration, measured as a function of $\mathit {Wi}$ , point to a critical slowing down at the coil–stretch transition. Importantly, these results show no qualitative change when chains in a turbulent flow are replaced by dumbbells in a Gaussian flow, thereby supporting the use of the latter for reduced-order modelling.

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Section: Introductionmentioning

confidence: 84%

Section: Discussionmentioning

confidence: 99%

“…2016; Valente, da Silva & Pinho 2016; Rosti et al. 2023) and experimental (Vonlanthen & Monkewitz 2013; Zhang et al. 2021).…”

Section: Stationary Statistics Of Polymer Stretchingmentioning

confidence: 99%

Section: Stationary Statistics Of Polymer Stretchingmentioning

confidence: 99%

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Polymers in turbulence: stretching statistics and the role of extreme strain rate fluctuations

Picardo,

Plan,

Vincenzi

2023

J. Fluid Mech.

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“…As De increases to 1, the scaling behaviour is modified: an increasing amount of energy is transferred by the elasticity of the polymers, which alters the spectra to achieve a different scaling coefficient p = −2.3. Such a scaling behaviour has been elucidated already in non-Newtonian flows without dispersed particles, and has been addressed as an 'elastic scaling' in experimental and numerical studies (Zhang et al 2021;Rosti, Perlekar & Mitra 2023). The range of k over which the scaling is valid is called the 'elastic' range, and this case turns out to be a clear case of the interaction of elastic and inertial turbulence.…”

Section: Flow Dynamicsmentioning

confidence: 94%

The dynamics of fibres dispersed in viscoelastic turbulent flows

Aswathy,

Rosti

2024

J. Fluid Mech.

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This study explores the dynamics of finite-size fibres suspended freely in a viscoelastic turbulent flow. For a fibre suspended in Newtonian flows, two different flapping regimes were identified by Rosti et al. (Phys. Rev. Lett., vol. 121, issue 4, 2018, 044501): one dominated by time scales from the flow, and another dominated by time scales associated with its natural frequency. We explore in this work how the fibre dynamics is modified by the elasticity of the carrier fluid. For this, we perform direct numerical simulations of a two-way coupled fibre–fluid system in a parametric space spanning different Deborah numbers, fibre bending stiffness (flexible to rigid) and linear density difference between the fibre and the flow (neutrally buoyant to denser-than-fluid fibres). We examine how these parameters influence various fibre characteristics such as the frequency of flapping, curvature, and alignment with the fluid strain and polymer stretching directions. Results reveal that the neutrally buoyant fibres, depending on their flexibility, oscillate with large and small time scales transpiring from the flow, but the smaller time scales are suppressed as the polymer elasticity increases. Polymer stretching is uncommunicative to denser-than-fluid fibres, which flap with large time scales from the flow when flexible, and with their natural frequency when rigid. Thus the characteristic elastic time scale has a subdominant effect when the fibres are neutrally buoyant, while its effect is absent when the fibres become more inertial. In addition, we also explore the fibre's bending curvature and its preferential alignment with the flow to identify the other roles of viscoelasticity in modifying the coupled fluid–structure dynamics. Inertial fibres have larger curvatures and are less responsive to the polymer presence, whereas the neutrally buoyant fibres show quantitative changes. The perceptible passivity of the denser fibres is again reflected in the way they align preferentially with the polymeric stretching directions: the neutrally buoyant fibres show a higher alignment with the polymer stretching directions compared to the denser ones. In a nutshell, the polymers exert a larger influence on neutrally buoyant fibres, which are more reflective of the polymeric influence in the flow. The study addresses comprehensively the interplay between polymer elasticity and the fibre structural properties in determining its response behaviour in an elasto-inertial turbulent flow.

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Turbulent/Non-turbulent Interface in Water Jet with Polymer Additives

Xi,

Peng,

Zhang

2024

IUTAM Bookseries

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The effect of polymer additives on the global entrainment of a turbulent round jet was found to show two distinct regimes: the reduction and enhancement regimes in the near and far fields, respectively. Using time-resolved simultaneous particle image velocimetry and laser-induced fluorescence measurements, we hereby present an experimental study on the local entrainment and engulfment process along the turbulent/non-turbulent interface (TNTI). We find that the local entrainment velocity is augmented in both regimes, due to the contribution from polymer elastic stress and a higher probability for TNTI to visit jet centreline region where the entrainment velocity is larger. In the entrainment reduction regime, the fractal dimension and length of TNTI are smaller compared to the Newtonian case; while those in the enhancement regime are nearly not changed. The difference between the two regimes results from the fact the jet flow decays in the streamwise direction. In the near field, the flow is intense enough to substantially stretch polymers, which results in a redistribution of energy among different scales and a steeper decay of energy in the inertial range. However, in the far field, the stretching of the polymer and in turn the feedback of polymers is not strong enough to alter the inertial range scaling of the energy spectrum. Moreover, our study reveals although more ambient fluid is engulfed into the turbulent region due to the augmented large scale motion by polymers, engulfment is still not the major contribution to the entrainment in polymer-laden jet, which is similar to the case in Newtonian jet.

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Large is different: Nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers

Cited by 12 publications

References 66 publications

Polymers in turbulence: stretching statistics and the role of extreme strain rate fluctuations

Polymers in turbulence: stretching statistics and the role of extreme strain rate fluctuations

The dynamics of fibres dispersed in viscoelastic turbulent flows

Turbulent/Non-turbulent Interface in Water Jet with Polymer Additives

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