Direct Numerical Simulation of Shear-Thinning and Thickening Power-Law Fluids in Rough-Walled Turbulent Flow

Direct numerical simulations (DNS) of turbulent power-law (PL) fluid flow over rough surfaces are performed for shear-thinning, Newtonian, and shear-thickening fluids. The focus is placed on understanding the impact of rheological behavior on turbulence characteristics and drag response in rough-wall channels. In the absence of published DNS data for PL fluids under these conditions, the present work addresses a significant knowledge gap. Validation is conducted for the Newtonian case using available rough-wall literature results, providing a reference baseline for the evaluation of non-Newtonian effects.

The results indicate that shear-thinning fluids produce notable modifications in the flow near roughness elements. In particular, the recirculation bubble formed between two consecutive rough elements is found to be mildly influenced by the decrease in the power-law index. Additionally, shear-thinning behavior alters the turbulent dynamics in the fully rough regime. While classical theory predicts that the friction factor reaches a plateau at high Reynolds numbers in rough-wall flows, the present simulations suggest that such a plateau may not occur for shear-thinning fluids, as the friction factor continues to exhibit Reynolds number dependence. This finding highlights a fundamental departure from Newtonian behavior and raises new questions about drag behavior in non-Newtonian turbulence.

In contrast, the shear-thickening case exhibits behavior qualitatively similar to high-Reynolds-number Newtonian flows, including more intense near-wall turbulence activity. These similarities suggest that shear-thickening PL fluids may be used to investigate Newtonian-like turbulence at lower Reynolds numbers, offering potential computational savings in high-fidelity studies.

To support the analysis, an analytical expression extending the classical Blasius 1/7 velocity profile to power-law fluids over rough walls is proposed and evaluated using the DNS results. This expression offers a generalized formulation for predicting the mean velocity field across different rheologies. Finally, comprehensive turbulence statistics are presented, enabling (for the first time) a detailed and systematic investigation of turbulent PL flows over rough surfaces.