Multistage transitions in viscoelastic turbulent flow: Vortex structures and self-sustaining mechanisms

Viscoelastic dilute polymer solutions are known to display drag reduction in turbulent flows. At constant Re and as the fluid becomes more elastic (increasing Wi), the flow undergoes transitions between several stages of different behaviors. The first is the onset of drag reduction, before which the turbulent friction factor remains indistinguishable from its Newtonian limit. The second is the transition from low-extent (LDR) to high-extent drag reduction (HDR), which increasing evidences have shown to be a qualitative transition between different types of turbulent dynamics. The third is the convergence to the maximum drag reduction (MDR) asymptote, after which the friction factor becomes constant. Although increasing drag reduction with increasing Wi is intuitively expected, transitions between these stages are accompanied by drastic changes in flow statistics and structural patterns, indicating fundamental differences in the underlying turbulent dynamics. Mechanistic understanding into these transitions is far from complete. Our latest work has offered fresh insights into both the LDR-HDR and HDR-MDR transitions. For the former, we developed a new vortex analysis method, called VATIP, and applied it to analyze the differences between the conformation statistics in LDR and HDR regimes. The result links the occurrence of HDR to the dominance of a new turbulence self-sustaining mechanism. For the latter, although a full answer to the MDR problem remains elusive, our analysis of the so-called elastoinertial turbulence (EIT) challenges the long-held presumption of MDR being an ultimate flow state that is no longer affected by polymers. The finding calls for a new direction of thought in constructing a theoretical explanation for MDR.