Laminar turbulent behavior in shear-thickening channel flow

We conduct direct numerical simulations (DNS) to investigate the dynamics of a non-Newtonian shear-thickening fluid in a turbulent plane channel. The primary parameter governing the non-Newtonian flow rheology is the Carreau number (Cu), defined as the ratio of the fluid’s characteristic timescale, Λ, to the flow characteristic timescale, h/uτ, where h is the channel half-height and uτ is the friction velocity at the wall. Starting from a Newtonian turbulent channel flow at Reτ = 180, we examine the impact of increasing Cu on turbulent statistics and coherent structures. The shear-dependent rheology is described using a Carreau viscosity model, with Cu values spanning two orders of magnitude (Cu = 0.1, 1, 5, 10). While maintaining a constant mean pressure gradient (∇ p) that drives the flow—ensuring a fixed shear Reynolds number based on the zero-strain-rate reference viscosity Reτ0 = 180—,we observe varying effective Reynolds numbers (Reτ,w = 111, 76, 58, 52) due to the altered viscosity distributions. Our findings reveal that shear thickening generally reduces the mean flow velocity and enhances the isotropy of velocity fluctuations compared to the Newtonian reference case. As Cu increases, the strength of vortical structures diminishes, accompanied by a decline in turbulence intensity. This behavior is primarily attributed to elevated wall viscosity, which shifts turbulent stresses towards viscous stresses. Notably, at subcritical effective shear Reynolds numbers for which a Newtonian fluid would exhibit laminar flow, the shear-thickening fluid retains unsteady behavior (turbulence) but lacks a logarithmic layer.