Friction loss for newtonian and power – Law fluids in expanding and contracting duct flows using the lattice boltzmann method

Abstract

This study investigates the hydrodynamic behavior of Newtonian and power-law non-Newtonian fluids in a channel with a contraction–expansion–contraction configuration, using the Lattice Boltzmann Method (LBM). Unlike previous research focused on isolated discontinuities, this work introduces a more realistic geometry to capture complex transient phenomena such as vortex formation, flow separation, and shear stress redistribution. Numerical simulations were conducted on a two-dimensional domain and validated against the analytical Poiseuille solution, showing relative errors below 2 %. The analysis was divided into three zones: entrance (A), expansion (B), and contraction (C). In Zone A, the product fRe converged toward the theoretical value of 64, confirming fully developed laminar flow. The head loss coefficient K exhibited a decreasing trend with the generalized Reynolds number, depending on the flow behavior index n. A two-K model was fitted to the data with excellent agreement (relative error below 0.001 %), and the parameters were generalized as functions of n, allowing predictions for fluids beyond those explicitly simulated. In Zone B, the sudden expansion induced complex flow reorganizations, with vortex formation and local recirculation. Although no predictive model was established for this region due to nonlinear and transient effects, the behavior was interpreted using rheological principles. Unlike conventional approaches that artificially fix the Reynolds number, this study applies a constant body force (F) —physically equivalent to a pressure gradient— allowing the generalized Reynolds number (Re_g) to emerge naturally from fluid rheology (n, k) and flow geometry. This approach demonstrates how rheology modulates flow reorganization under realistic driving conditions, offering a more faithful representation of flow-rheology interactions in CEC configurations. Overall, the results provide a predictive framework for energy loss assessment in systems combining abrupt geometric discontinuities (sudden expansions/contractions) with complex rheological behavior (from pseudoplastic to dilatant fluids), with direct applications in biomedical devices, food processing, and non-Newtonian fluid transport systems.