LAUSR

We numerically study the fluid dynamics of laminar, rheological flow in regular polygonal ducts. We demonstrate that the entry length for the flow development increases with a decrease in the number of sides m and an increase in flow behavior index n. Furthermore, we explore the impact of m and n on the major output parameters and propose simple correlations to predict entry length, the shape of the fully developed axial velocity profile and friction factor based on two newly introduced geometric parameters, viz., the factor of approach and integrity index. While it was well-known that turbulent flow through non-circular ducts typically induces Prandtl's secondary flow of the second kind, the present study reveals the occurrence of such secondary flow associated with the corner convexities of the primary velocity profile, even within the laminar regime. We capture a counter-rotating vortex pair at each corner of the polygonal duct as evidence of the secondary flow. A novel visualization method tracks the evolution of vortices diminishing downstream. The strength of the vortices reduces with the increase in the number of corners, as does the strength of secondary velocity. We demonstrate three distinct fluid dynamic regimes using the vortex line representation: the near-wall region, the inner core, and an intermediate region. The inner core and the intermediate region carry the signatures of potential and secondary flow regimes, respectively. These two regimes wipe out once the entire cross section becomes viscous-dominated, yielding a fully developed flow. Such development happens far from the duct's inlet for shear-thickening fluids.