Instability investigation of creeping viscoelastic flows between the rotating cylinders

In this paper, instability in the creeping viscoelastic flow between the rotating cylinders is investigated numerically. Due to the low speed of flow field, the second order fluid (SOF) model is used as the constitutive equation and the governing equations are solved by a second order finite difference method based on the artificial compressibility algorithm in a staggered mesh. The effects of normal stress differences on the flow stability are investigated for a wide range of gap ratios. Unlike the previous studies, the origin and mechanism of flow instability resulted from normal stress differences are investigated in detail. Numerical results indicate that the hoop stress and radial-normal stress components are appeared in viscoelastic flows between the rotating cylinders and they have an important role on the flow stability.