Turbulent channel flow of generalized Newtonian fluids at a low Reynolds number

Several studies concerning the turbulent pipe flow of generalized Newtonian (GN) fluids may be found in the literature, but not for channel flow, although that has been extensively studied for other types of non-Newtonian fluids, such as those with viscoelastic effects. Direct numerical simulations corresponding to statistically converged turbulent channel flow of GN fluids at a low frictional Reynolds number have been performed. The shear-dependent viscosity is introduced through the Carreau fluid model, and results corresponding to the Newtonian fluid case are compared to those of moderate shear-thickening and shear-thinning fluid behaviour. The different statistics studied reveal that shear-dependent fluid rheology appears mainly to affect the flow within the inner layer region and with shear-thinning behaviour; suppressing near-wall structures such as quasi-streamwise vortices and low-speed streaks, inhibiting turbulence generating events and leading to different drag reduction features. These include: enhancement of streamwise turbulence intensity and suppression of the other cross-sectional intensities, decrease of the Reynolds shear stress (leading to a lessening in turbulent production), decrease in energy redistribution between individual components of the Reynolds stress tensor through the velocity-pressure gradient term and overall increase in turbulence anisotropy at both small and large scales. In particular, it is noted that at the channel centre 'rod-like' turbulence states, a known low-Reynolds-number behaviour, are more clearly seen with shear-thinning fluid rheology.