Experimental observation of the elastic range scaling in turbulent flow with polymer additives

Abstract

A minute amount of long-chain flexible polymer dissolved in a turbulent flow can drastically change flow properties, such as reducing the drag and enhancing mixing. One fundamental riddle is how these polymer additives interact with the eddies of different spatial scales existing in the turbulent flow and, in turn, alter the turbulence energy transfer. Here, we show how turbulent kinetic energy is transferred through different scales in the presence of the polymer additives. In particular, we observed experimentally the emerging of a previously unidentified scaling range, referred to as the elastic range, where increasing amount of energy is transferred by the elasticity of the polymers. In addition, the existence of the elastic range prescribes the scaling of high-order velocity statistics. Our findings have important implications to many turbulence systems, such as turbulence in plasmas or superfluids where interaction between turbulent eddies and other nonlinear physical mechanisms are often involved.

Large is different: non-monotonic behaviour of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers

“…Here we present evidence, from the highest resolution simulations of polymeric fluids, that indeed there is a range of scales r over which the structure function S 2 (r) seems to show scaling consistent with recent experimental results [1]. We also show that the new scaling is a purely elastic effect, and that this elastic behaviour is non-monotonic in Deborah number.…”

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We use high resolution direct numerical simulations to study statistically stationary, homogeneous, and isotropic turbulent flows of dilute solutions of polymers at high Reynolds numbers and Deborah numbers. We find that for small wavenumbers k, the kinetic energy spectrum shows Kolmogorov-like behavior which crosses over at a larger k to a novel, elastic scaling regime, E(q) ∼ k −ξ , with ξ ≈ 2.3, providing support to and extending the analysis of recent experimental results [1]. We uncover the mechanism of elastic scaling by studying the contribution of the polymers to the flux of kinetic energy through scales.

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“…Eventually, the elastic range practically disappears at De ≈ 5 -the classical Kolmogorov range is restored. This remarkable behavior is better elucidated by plotting the two compensated spectra k 5/3 E(k) and Although, the steepening of the spectra beyond a certain wavenumber k = k p have been observed before in both direct numerical simulations [9,11,18,19,27] and experiments [33], this was mostly confined to the dissipation range due to the small separation of scales related to the Reynolds number considered; only recent experiments [1], for the first time. demonstrated the emergence of this elastic scaling.…”

“…Nevertheless, there can be net reduction of the dissipation of kinetic energy [6][7][8][9][10][11][12] because the presence of polymers changes the turbulent cascade qualitatively. Significant theoretical [3,5,[13][14][15], numerical [9,11,12,[16][17][18][19][20][21][22][23][24][25][26][27], and experimental [1,6,[28][29][30][31][32][33] efforts have gone into elucidating the nature of the turbulent energy cascade in the presence of polymers. It is now reasonably well established [9,11] that for large enough scale separation between the energy injection scale, L inj , and the Kolmogorov scale, L K , there exists an intermediate scale L p such that for scales L p < r < L inj the * marco.rosti@oist.jp energy cascade is practically the same as that of a Newtonian flow, with the shell-integrated energy spectrum being E(k) ∼ k −5/3 and the second order structure function S 2 (r) ∼ r 2/3 .…”

“…This question could not be probed with the low-Reynolds and low-Deborah simulations quoted above. Recent experiments [1] had tentatively suggested that a new scaling range indeed appears, although the evidence is not yet unequivocal. Experiments [1,37] also showed that, contrary to Lumley's arguments [38], the scale L p does depends on concentration of polymers.…”