Instability Investigation of Taylor-Couette Flow with an Axial Velocity by D Chebychev Tau-Method

Instability of a viscous incompressible flow between two rotating concentric cylinders has been investigated numerically. The outer cylinder is stationary and the inner one rotates and moves axially simultaneously. D Chebychev tau method is used to solve eigenvalue problem governing the investigation of flow stability, In the Chebychev tau method, the eigen functions of governing equations are expressed in terms of Chebychev polynomials and the generalized eigenvalue problem is solved with the QZ algorithm. It should be mentioned that this method is a new approach to solve instability of spiral Couette flow and it is less time consuming and more direct than the methods used by previous workers. The applied method is so efficient and our results are in a very good agreement with pervious works. The critical flow characteristics are calculated at the threshold of instability for various Reynolds number based on the axial velocity. The results point out that the axial velocity increases the flow stability. Also, it is found that the axisymmetric modes are more unstable than the corresponding non-axisymmetric modes for all of Reynolds number.