Effect of Weissenberg number on polymer-laden turbulence

Rehman, Sajjad ur; Lee, Junghoon; Lee, Changhoon

doi:10.1103/physrevfluids.7.064303

Cited by 2 publications

(6 citation statements)

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“…2010; ur Rehman et al. 2022). Clearly, the reduction in the mean strain rate will cause two-way coupled polymers to stretch less, on average, than one-way coupled passive polymers.…”

Section: Discussionmentioning

confidence: 99%

“…It should be noted that the simulations of ur Rehman et al. (2022) were carried out at a low volume fraction; the impact of feedback forces on polymer stretching may differ at larger volume fractions.…”

Section: Discussionmentioning

confidence: 99%

“…This insight has relevance for the extension of polymers in the presence of two-way coupling with the flow. The feedback forces exerted by polymers onto the flow not only reduce the mean value of the strain rate but also suppress its extreme-valued fluctuations (Perlekar et al 2010;ur Rehman et al 2022). Clearly, the reduction in the mean strain rate will cause two-way coupled polymers to stretch less, on average, than one-way coupled passive polymers.…”

Section: Discussionmentioning

confidence: 99%

“…Would we see a separate effect of the loss of extreme events, arising from just the change in the shape of the distribution of strain rates? This question was addressed in recent Eulerian-Lagrangian simulations by ur Rehman et al (2022). They defined an effective Wi for two-way coupled polymers, using the reduced value of the Kolmogorov time scale of the modified flow, and then compared the stretching statistics of two-way and one-way coupled polymers.…”

Section: Discussionmentioning

confidence: 99%

“…To our knowledge, however, the effect of the strongly non-Gaussian fluctuations of a turbulent velocity gradient on the statistics of R, and in particular on the dependence of α upon Wi, has not yet been investigated. With this aim, we carry out Lagrangian numerical simulations of finitely extensible nonlinear elastic (FENE) dumbbells in three-dimensional isotropic turbulence, as well as in a Gaussian model of the velocity gradient, and compare the statistics of R. This investigation has relevance beyond stochastic modelling, because flows without extreme strain rates arise naturally in the context of polymer solutions -wherein polymer feedback forces suppress extreme velocity gradient fluctuations (Perlekar, Mitra & Pandit 2010;Watanabe & Gotoh 2013;ur Rehman, Lee & Lee 2022).…”

Section: Introductionmentioning

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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“…2010; ur Rehman et al. 2022). Clearly, the reduction in the mean strain rate will cause two-way coupled polymers to stretch less, on average, than one-way coupled passive polymers.…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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