Numerical modelling of non-Newtonian laminar flow in partially-filled pipe

The prediction of the fully developed laminar flow of non-Newtonian slurries in partially-filled pipes is a key challenge for many industries, including mining and nuclear. Within the nuclear industry, reprocessing waste frequently occurs as a shear-thinning slurry, and understanding its transportation is critical for maintaining operational safety and environmental protection. In this work, a validated Computational Fluid Dynamics (CFD) analysis of these challenging flows is presented, focusing on the interaction between fluid rheology and partially-filled pipe flow.

Our approach consists of modelling shear-thinning behaviour using power-law and Cross models, and yield-stress behaviour using Bingham and Herschel-Bulkley models. The parameter space is examined by varying the power-law index (n), the Carreau number (Cu), and the Bingham number (Bn) over a wide range of values, across 14 fill heights (25-95% of pipe diameter) in subcritical laminar flow (Fr<1, Re‌<2100). The CFD model is validated against the analytical solutions for Newtonian flow in partially-filled pipes, the analytical solutions for full-pipe power-law and Herschel-Bulkley flow, and new laser Doppler velocimetry (LDV) measurements at different fill heights in a full-scale pipe rig with xanthan gum (XG) and Carbopol (CB) solutions as model Cross (XG) and Herschel-Bulkley (CB) fluids.

A key result is found in the secondary-flow-induced velocity dip, a well-known phenomenon in Newtonian partially-filled pipe flows where the maximum velocity is below the free surface. Our findings show that although this effect is still present in non-Newtonian flow at high fill heights (>85%), its magnitude is greatly diminished as the fluid becomes more shear-thinning, and the velocity profile becomes flatter. For strongly shear-thinning fluids, the velocity dip is completely suppressed, and the maximum velocity returns to the free surface. The study offers an understanding of how non-Newtonian rheology influences flow in a partially-filled pipe, improving the optimisation of slurry transport and supporting safety requirements of the nuclear sector.