Structure and dynamics of turbulence in viscoelastic channel flow

Michael D. Graham,

University of Wisconsin-Madison

Abstract

Addition of a small amount of long-chain polymer to a liquid renders it viscoelastic and leads to dramatic reduction of energy dissipation in the turbulent flow regime -- the phenomenon of rheological drag reduction. We are interested here in how viscoelasticity alters the flow structures observed in Newtonian turbulent flows, as well as how it leads to the formation of new structures not observed in the Newtonian case.

The dominant near-wall structure of Newtonian turbulence is wavy streamwise vortices. Using direct simulations in channel flow, we illustrate how these are affected by viscoelasticity. We observe occasional nearly quiescent "hibernating" intervals with very weak, and weakly streamwise-dependent structure, separated by intervals of "active" turbulence with strong streamwise vortices and three-dimensionality. With increasing Weissenberg number, Wi, the active intervals are strongly suppressed, while the hibernating ones are only weakly affected. A simple mechanistic theory captures key features of the intermittent dynamics observed in the simulations.

If the Reynolds number is sufficiently low, the flow will relaminarize as Wi increases further, but then given a small but finite perturbation, will become turbulent again, with features that are very different from Newtonian turbulence. This regime has been denoted ''elastoinertial turbulence" (EIT). In the parameter range we consider, we show that EIT at low Re has highly localized stress fluctuations that strongly resemble the viscoelastic extension of so-called Tollmien-Schlichting (TS) modes. This is a bit of a surprise: while Newtonian channel flow exhibits a two-dimensional linear instability due to growth of TS modes, the resulting flow structure bears no resemblance to Newtonian near-wall turbulence, so TS modes are not traditionally viewed as playing an important role in turbulence. These results suggest that, in the parameter range considered here, the bypass transition leading to EIT is mediated by nonlinear amplification and self-sustenance of perturbations that excite the viscoelastic TS mode.

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