Study of the Rheological Behaviour and the Curvature Radius Effects on a Non Newtonian Fluid Flow in a Curved Square Duct

Abstract. Fluid flows through curved pipes are frequently encountered in various industrial or biomedical applications. These flows, under the effect of the centrifugal force resulting from the curvature of the pipe, causes an instability phenomenon known as Dean instability, which results in the appearance of two or more counter-rotating vortex cells. The objective of this work is to determine numerically the effect of geometric parameters and rheological behavior of the fluid, including the index of behavior on the occurrence and development of the instability of Dean in a 180° curved duct. The governing equations including the full Navier-Stokes, the continuity and the Momentum are solved in three dimensions using the commercial code ANSYS-CFX, under the conditions of laminar, stationary and incompressible flow. In the first part, the results of the flow of a shear thinning fluid and a shear thickening fluid for a Dean number Dn = 125 and a radius of curvature Rc = 15.1 are presented. These calculation results gave a good agreement with the measured values extracted from the literature. The second part concerns the influence of the curvature ratio and the rheological behaviour of the fluid, the presence of two stationary secondary recirculations, as well as the appearance and the development of two additional vortices are highlighted. The main point observed is that the decrease in the curvature radius increases the instability of the flow through the pipe and this increases the number of vortex cells (Dean vortex). The velocity of the flow and its rheological nature are essential parameters for the reduction of instability in the canal.