Turbulent wall-bounded flow of weakly shear-thinning fluid: Phenomenological modeling of eddy viscosity and law of the wall

This work proposes a new analytical law of the wall for turbulent, wall-bounded flows of generalized Newtonian fluids. Direct numerical simulation data from the literature are processed to analyze and model the total (molecular + turbulent) viscosity profiles in pipe flows for power-law fluids with flow indices in the range 0 . 4 < n < 0 . 8 and generalized Reynolds numbers between 11 × 1 0 3 and 20 × 1 0 3 . The total viscosity is expressed as a nonlinear function of the wall-normal coordinate y + , revealing a deviation from the classical linear dependence valid for Newtonian fluids. A simplified empirical formulation of the turbulent viscosity is proposed, leading to a non-logarithmic mean velocity profile that captures the effects of shear thinning. The resulting analytical velocity profiles show good agreement with literature data and reproduce the observed upward shift of the mean velocity in the near-wall region. From this law, expressions for the Fanning friction factor and drag reduction coefficient are derived. The analysis captures the drag reduction increase with decreasing flow index and decreasing generalized Reynolds number, consistent with the low drag reduction (LDR) regime reported in previous numerical studies. In order to generalize our results, it will be necessary to explore a wider range of flow indices and Reynolds numbers. • New model of axial mean velocity wall law for turbulent shear-thinning fluid flows. • Nonlinear eddy viscosity model derived from DNS data. • Analytical friction factor validated with DNS data. • Drag reduction factor expression for low drag reduction regime (LDR).