Instability Investigation of Taylor-Couette Flow with an Axial Velocity

This paper investigates instability of a viscous incompressible fluid between two infinite concentric cylinders. The outer cylinder is stationary but the inner one rotates and moves in axial direction simultaneously. To solve the eigenvalue problem governing the investigation of flow stability, D4 Chebychev tau method is applied. 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. 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.

کلیدواژه ها:

instability ، Chebyshev tau methods ، Taylor-Couette flow