ON THE EFFECT OF CORNER CURVATURE IN LAMINAR FLOW THROUGH A CROSS-SLOT CHANNEL

Abstract. The flow of viscoelastic liquids through a cross-slot geometry is studied by means of numerical simulations. The geometry is planar and the constitutive model follows the FENE-CR (constant shear viscosity) equation, valid for relative dilute solutions of polymeric fluids, under fully developed flow conditions. A fully implicit finite-volume numerical method is used to solve the governing equations. For Deborah numbers above a critical value (dependent on the extensibility parameter of the model L 2 and the solvent viscosity ratio β) the flow becomes asymmetric but remains steady. This effect is solely due to the elastic nature of the flowing fluid, i.e. the instability is purely elastic in nature. The main objectives of the present study are: to examine the possible effects of rounding the corners of the geometry (curvature radius of R = 0.05d and 0.5d, where d is the channels ’ width) for a range of values of the controlling non-dimensional parameters (De, L 2 and β); to calculate the critical Deborah number of th