Effect of Power-Law Index and Shape on the Onset of Flow Separation

Abstract

The present work investigates the first flow regime transition, namely, the onset of flow separation from the surface of a submerged body, for power-law fluids (shear-thinning and shear-thickening fluids) for a range of axisymmetric shapes. In particular, the geometries considered here include spheroids, hemisphere, spherical caps, cones, conical caps, frustum of cones and disks in two orientations with respect to the direction of the flow. Broadly, this transition occurs at progressively lower Reynolds numbers for objects with reduced degree of streamlining, or in the presence of geometric singularities (corners) and a high level of curvature, even in Newtonian fluids. The role of body shape is further accentuated for power-law fluids due to the variation in the fluid viscosity along the surface, as well as its spatial variation. For shear-thinning fluids (n<1), the critical Reynolds number exhibits a peak somewhere around n-0.4-0.5 for each shape studied here, and this is attributed to the interaction between the non-linear viscous and inertial forces prevailing in the flow field. For shear-thickening fluids, it progressively decreases with the increasing value of power-law index.