Reynolds number effects in pipe flow turbulence of generalized Newtonian fluids

The turbulent pipe flow of inelastic shear-thinning fluids has many practical applications; however, there is a deficit in understanding of how shear-thinning rheology modifies turbulence structure in the near-wall boundary layer (affecting shear stress and pressure drop) and in the core (affecting mixing). While previous direct numerical simulation studies have examined the effect of shear-thinning rheology at low Reynolds number (Re-tau,Re-max = 323), the way in which these effects vary with Re-tau was unknown. In particular, from earlier work it was unclear if inner-scaled mean axial velocity profiles for Newtonian and shear-thinning fluids could collapse to a common curve with increasing Reynolds number. Via direct numerical simulations of Newtonian and one shear-thinning rheology for friction Reynolds number Re-tau = 323-750 (Re-G = 10 000-28 000), the present study investigates how increasing Reynolds number modifies turbulent pipe flow of a power-law fluid with particular focus on the boundary layer profiles. The results show that the inner-scaled mean axial velocity profiles for Newtonian and shear-thinning fluids cannot collapse to a common curve with increasing Reynolds number, which is consistent with predictions from the Dodge-Metzner correlation [Dodge and Metzner, Turbulent flow of non-Newtonian systems, AIChE J. 5, 189 (1959)]. In inner-scaled coordinates, mean viscosity profiles are shown to become independent of Reynolds number except close to the pipe center. The contribution of viscosity fluctuations in the mean shear budget and in the mean flow and turbulence kinetic energy budget remains small at all Re. Both increasing Reynolds number and shear thinning influence the turbulence kinetic energy budget near the wall; however, the region where shear thinning is important is much wider than the region where increasing Reynolds number influences the results. The persistence of shear-thinning effects on turbulence modification in pipe flow requires consideration in the development of suitable turbulence models for such fluids. The current results suggest that the effect of shear-thinning rheology in turbulence models can be captured via a Reynolds-number-independent mean viscosity model in the inner region.