Numerical solution for the flow of viscoelastic fluids around an inclined circular cylinder.

Abstract

The hydrodynamic force on an inclined circular cylinder of finite length in a uniform flow has been calculated numerically from the steady velocity field around the cylinder predicted in Part I, and the influence of shear thinning and elasticity on the hydrodynamic force and the attitude variation of a slender body has been discussed.

The shear thinning behavior greatly reduces the fluid viscosity adjacent to the cylinder, in turn reduces drag force. In addition, an increase in viscosity compensates to some extent for a decrease in velocity gradient on the cylinder surface. Therefore, the moment acting to rotate the cylinder into a perpendicular orientation to the incoming flow decreases with an increase in shear thinning. While elasticity has little effect on shear stress, it strongly affects normal stress and the drag force due to the normal stress becomes larger as elasticity increases. This elastic effect is especially remarkable near both ends of the cylinder.

When only shear thinning is taken into account, the moment acts in such a way as to rotate the cylinder into a perpendicular orientation to the flow. In contrast to this result, the moment acting to rotate the cylinder into a parallel orientation to the flow can be predicted when not only shear thinning but also elasticity are taken into account. Thus, the present numerical analysis for the hydrodynamic force on an inclined cylinder is valid to explain the mechanism of the attitude variation of a slender body falling in polymer solutions.