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The existence of a maximum drag enhancement (MDE) asymptote at high rotation ($Ro$) and Weissenberg ($Wi$) numbers in turbulent viscoelastic spanwise-rotating plane Couette flow has been demonstrated. Specifically, it is shown that above a critical $Wi$, drag enhancement plateaus and the MDE asymptote is realized in a broad range of $Ro$. The mean velocity profiles at MDE appear to closely follow a log-law profile that has a nearly identical slope but different intercepts as a function of $Ro$. Much like the maximum drag reduction (MDR) asymptote, the logarithmic function in MDE is closely followed if the mean velocity is plotted using the traditional inner variable scaling; however, the logarithmic function is not well defined when examined by the indicator function. Hence, in this study, we have used the logarithmic fit as a visual guide for the mean velocity profile. Last and perhaps the most intriguing finding of this study is that MDE occurs in the elasto-inertial turbulence (EIT) flow state; hence, it is mainly sustained by elastic forces much like the MDR flow state. To that end, a universal picture of elastically induced drag modification asymptotes is emerging, namely these asymptotic states are an inherent property of the elastically sustained EIT flow state.
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 $Ro=0.5 - 0.9$.
Direct numerical simulation of polymer-induced flow relaminarization of turbulent spanwise-rotating plane Couette flow (RPCF) is reported for the first time. Specifically, the reverse transition pathway from a Newtonian turbulent RPCF to a fully relaminarized drag enhanced viscoelastic flow has been elucidated. Evidently, this transition occurs gradually by weakening and eventual elimination of small-scale vortices as the Weissenberg number ($Wi$) is enhanced, paving the way for a two-dimensional laminar flow consisting of large-scale and highly organized roll cells. The influence of polymer additives on convective momentum exchange by large-scale roll cells and small-scale turbulent vortices, namely, the drag reduction (DR) realized by elimination of turbulent vortices and the significant drag enhancement (DE) that results from polymer roll cell interactions has been identified as the mechanism of DE. The observed vortical changes point to a universal mechanism for the coupling of polymer chains and turbulent vortices in wall-bounded viscoelastic DE and DR flows.
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