Influence of smooth constriction on microstructure evolution during fluid flow through a tube

A numerical solution for axis-symmetrical fluid flow through a smooth constriction using the alternating direction implicit finite volume method and the fractional-step-method is presented. The wall is modelled with a smooth contraction mapped by a sinusoidal function and the flow is supposed to be axis-symmetric. A pressure boundary condition is set at the inlet and the resulting pressure gradient field drives fluid flow which is always in laminar regime. This study presents results for a non-Newtonian fluid using the Ostwaldde Waele constitutive model. Moreover, a transient network representing three different microstructures, immersed in the fluid, is evolved by viscous dissipation and an isothermal process is considered. The time dependent evolution of the transient network is represented by a set of kinetic equations with their respective forward and reversed constants. The numerical predictions show that, at a fixed Reynolds number, the viscous dissipation and the grade of structure restoration or breakage is influenced by constriction severity due to the energy generated during fluid flow. A 50% reduction in transversal section generates secondary flow downstream and vortex shedding, whereas a 10% and 25% constrictions presents a thin boundary layer and no secondary flow near the constricted wall.