Relaminarization of spanwise-rotating viscoelastic plane Couette flow via a transition sequence from a drag-reduced inertial to a drag-enhanced elasto-inertial turbulent flow

Abstract

Direct numerical simulation of spanwise-rotation-driven flow transitions in viscoelastic plane Couette flow from a drag-reduced inertial to a drag-enhanced elasto-inertial turbulent flow state followed by full relaminarization is reported for the first time. Specifically, this novel flow transition begins with a drag-reduced inertial turbulent flow state at a low rotation number $0\leqslant Ro \leqslant 0.1$ , and then transitions to a rotation/polymer-additive-driven drag-enhanced inertial turbulent regime, $0.1\leqslant Ro \leqslant 0.3$ . In turn, the flow transitions to a drag-enhanced elasto-inertial turbulent state, $0.3\leqslant Ro \leqslant 0.9$ , and eventually relaminarizes at $Ro=1$ . In addition, two novel rotation-dependent drag enhancement mechanisms are proposed and substantiated. (1) The formation of large-scale roll cells results in enhanced convective momentum transport along with significant polymer elongation and stress generated in the extensionally dominated flow between adjacent roll cells at $Ro\leqslant 0.2$ . (2) Coriolis-force-generated turbulent vortices cause strong incoherent transport and homogenization of significant polymer stress in the bulk via their vortical circulations at $Ro=0.5 - 0.9$ .

Vortex merging and splitting events in viscoelastic Taylor–Couette flow

“…In the simulations presented here, S c = 100, which yields an artificial diffusion coefficient, 1/ReS c = 10 −4 . This amount of diffusion is similar in magnitude to those used in other recent numerical studies on viscoelastic flows (Xi & Graham 2010;Lopez et al 2019;Song et al 2019;Zhu et al 2020;Song et al 2021b;Zhu et al 2022). It has been verified that a reduction in the amount of diffusion does not significantly alter the results of the simulations (Sc up to 200 were tested), thereby confirming the adequacy of the diffusion used for the simulations throughout the paper.…”

“…2021 b ; Zhu et al. 2022). It has been verified that a reduction in the amount of diffusion does not significantly alter the results of the simulations ( up to were tested), thereby confirming the adequacy of the diffusion used for the simulations throughout the paper.…”

Turbulent Taylor–Couette flow of dilute polymeric solutions: a 10-year retrospective

“…To that end, RPCF is an ideal flow to highlight similarities and differences between elastically induced turbulence in prototypical curvilinear and rectilinear shear flows. Hence, Liu, Khomami and co-workers have performed a comprehensive study to elucidate the mechanisms that give rise to drag modifications in viscoelastic TC and RPCF [32,37,38,54,58,77,78].…”

“…In the limit of zero curvature, i.e. (ηfalse→1), in viscoelastic RPCF [58,78], two DE mechanisms are at play: (i) for low system rotation (Ro≤0.2), formation of large-scale roll cells (figure 6 c ) that enhance convective momentum transport along with significant polymer elongation and stress generated in the extensionally dominated flow localized between neighbouring roll cells; (ii) for strong system rotation (Ro=0.5∼0.9), small-scale Coriolis-force-generated turbulent vortices (figure 6 d ) that cause strong incoherent transport and homogenization of significant polymer stress in bulk via their vortical circulations.

Figure 6Viscoelastic vortices visualized by averaged streamwise vorticity falsefalse⟨ωθ/xfalsefalse⟩θ/x,t in (r/y,z) plane.

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“…Specifically, Zhu et al. [78] have proposed a universal mechanism for all DR and DE flows, namely, the introduction of polymer additives tends to suppress vortical structures and in turn reduce the Reynolds shear stress production. Meanwhile, large-scale turbulent structures work to produce significant polymer stress to compensate the reduction of Reynolds stress.…”