Unsteady flow past rounded rectangular cylinder in power-law fluid: OpenFOAM simulations with proper orthogonal decomposition

This study presents a numerical investigation of unsteady flow past rectangular cylinders with rounded corners in power-law fluids at Reynolds number Re=150 (based on bulk inlet velocity U∞ and cylinder height D), corresponding to the unsteady laminar vortex-shedding regime under confinement and blockage ratio D/LH=0.2. Simulations were performed using the nonNewtonianIcoFoam solver in OpenFOAM for two aspect ratios (AR = 1 and 2), three corner radii (R/D=0, 0.25, 0.50), and three power-law indices (n=0.6, 1.0, 1.4) representing shear-thinning, Newtonian, and shear-thickening behaviors. The results demonstrate that increasing the corner radius significantly modifies the wake dynamics and reduces drag. For AR = 1 and n=0.6, the total drag coefficient decreased by up to 46.7% from R/D=0 to 0.5. At n=0.6, the Strouhal number exhibits a 55.4% increase as the corner radius ratio R/D rises from 0 to 0.5, indicating that corner rounding enhances wake stability and promotes more regular vortex shedding. Time-averaged pressure coefficient (Cp) contours showed enhanced base pressure recovery and shortened recirculation zones. Vorticity and Q-criterion fields revealed suppression of vortex shedding and wake unsteadiness at higher R/D and lower n. Proper orthogonal decomposition (POD) analysis showed that the first two modes captured over 85% of the total energy for rounded geometries, indicating dominance of coherent structures and enhanced flow regularity. The novelty of this work lies in its combined analysis of non-Newtonian effects, geometric rounding, and modal decomposition under confined unsteady conditions.