Three dimensional effects of Newtonian and viscoelastic fluids past a confined cylinder

Abstract

The 2D laminar flow around a confined cylinder with a 50% blockage ratio is an established benchmark in the development of numerical methods for non-Newtonian fluids [1]. Its practical application is accompanied by 3D flow characteristics and the combination of flow inertia, viscoelasticity and three-dimensionality leads to unexpected results. As such, the impact of 3D effects depends essentially on the aspect ratio of the cylinder, the type of confinement, the Reynolds number and also on the rheology of the working fluid. The study of viscoelastic flow past a confined cylinder in a rectangular duct with a blockage ratio of 50% shows the appearance of 3D effects near the end walls [2]. Studies of the flow past gradual contractions, which can be qualitatively compared with the upstream flow around a cylinder, show the appearance of velocity overshoots near the end walls upstream the contraction. This velocity overshoots, called cats ears phenomenon is due to elastic effects [3, 4]. Most of the experimental studies of viscoelastic fluid flow past a confined cylinder refer to steady creeping flow conditions or, in contrast, to high Reynolds number flows, close or above the onset of vortex shedding. So, the lack of experimental studies that consider flow around a cylinder from creeping conditions up the onset of laminar vortex shedding is one of the motivations of this work. The existence of 3D effects and their dependency with the aspect ratio is also an important aspect of our investigation. The main goal of this study is to investigate the flows of a Newtonian fluid and a viscoelastic shear-thinning fluid past a confined cylinder from creeping flow conditions (Re 0) up to the critical condition for the onset of vortex shedding. The Newtonian results obtained are compared with numerical calculations, using an in-house finite volume code [5].