Deflection of non-Newtonian simple shear flow around a rigid cylindrical body by the finite element method

Abstract

This paper describes flow during simple shear of non-Newtonian (power-law) viscous materials around a rigid cylindrical body, and examines how the magnitude of the stress exponent ( n) influences the deflection of particle paths as well as dynamic and kinematic quantities. A limited range of values (1–5) of n was used in the analysis. The angular velocity of the cylinder is half of the far-field shear strain rate, which is exactly the same as that for a Newtonian fluid. Particle paths always exhibit a ‘double-bulge shaped’ separatrix, the size of which slightly decreases with increasing n. The maximum values of pressure and differential stress also slightly decrease while that of vorticity and kinematic vorticity number increase as n increases, although the maximum change is less than 24% from n = 1 to n = 5. The general pattern of distribution of these dynamic and kinematic quantities around the cylinder for different values of n look similar. The non-Newtonian flows are, as a first approximation, similar to the Newtonian one.