Influence of Carreau number on relaminarization of turbulent Shear Thickening channel flow*

We investigate numerically the relaminarization of a turbulent non-Newtonian shear thickening fluid in a channel geometry. The flow of a shear thickening fluid is characterized by the Carreau number which is the ratio between, λ, the fluid characteristic time constant and the flow characteristic timescale based on the shear rate of the channel. Using Direct Numerical Simulation (DNS), we start from an initial Newtonian turbulent channel flow at shear Reynolds number Re=180 and we investigate the effect of increasing Carreau number on the turbulent statistics and coherent structures. The shear dependent rheology is modelled via a Carreau viscosity model, and we range Cu over three orders of magnitude: Cu = 0.1, 1,5,10. For the same mean pressure gradient ∇p, we obtain an effective shear Reynolds number based on the wall viscosity of Re=111,76,58,52 respectively. Results show that the mean flow velocity decreases and velocity fluctuations become more isotropic, leading to increased Reynolds stresses, relative to the Newtonian case. Increasing Cu, we observe a general decrease in the turbulence activity, induced by an increase in the wall viscosity, corresponding to a more rare presence of vortical structures and reflected by the turbulence modules. However, we observe that at the same low effective shear Reynolds, at which a Newtonian fluid would flow in laminar condition, the shear thickening flow still exhibits turbulence, without a logarithmic layer.