Velocity–vorticity correlations and the four-layer regime in turbulent channel flow of generalized Newtonian fluids

Abstract

The data of Arosemena et al. (2021), consisting of turbulent channel flow simulations of generalized Newtonian (GN) fluids, are considered to study the effects of shear-dependent rheology on the nonzero velocity–vorticity correlations and the mean dynamics. In the near-wall region and compared to Newtonian channel flow, the velocity–vorticity products contributing to the turbulent inertia term decrease/increase with shear-thinning/thickening fluid behaviour suggesting that with e.g. shear-thinning rheology, the sublayer streaks are more stable, the near-wall vortical motions are dampened and there is a narrower range of turbulent length scales. The mean momentum balance analysis, on the other hand, revealed that the four-layer structure first recognized by Wei et al. (2005a) remains for all GN fluids and that the shear-dependent rheology only seems to influence the location of the layers. For instance, with shear-thinning behaviour, layers II and III are thicker and there is an increase in the importance of the viscous forces in these intermediate layers. The influence of shear-thinning/thickening fluid behaviour on the extent of the layers II and III is found remarkably similar to an increase/decrease of the Reynolds number for Newtonian channel flow. These findings suggest that the shear-dependent rheology should also be taken into account for proper scaling of the intermediate layers. A potential length scale factor is proposed and its suitability is tested.