Stability of a viscous flow between rotating coaxial cylinders: Part 1: A numerical study of instability of flow between rotating cylinders. Part 2: Hydrodynamic instability of a viscous flow between rotating coaxial cylinders with main axial flow fully developed

An efficient numerical method is developed to predict the conditions for instability in a viscous fluid contained between rotating coaxial cylinders of arbitrary radius ratio (0.1-0.95). Explicit finite difference approximations are used to solve the perturbed Navier-Stokes equations which are in linear form. Computational procedure as well as boundary conditions are described, and results are reported in terms of the critical Taylor number and corresponding wave number. Cases in which the cylinders are rotating in the same direction as well as in opposite directions are analyzed. The results are compared with other analytical solutions. Streamline distributions are presented at the critical state for several cases examined. The results indicate regions of time dependent modes in the secondary flow for cases of counterrotating cylinders.