Global Stability Analysis of Eccentric Taylor Couette Flow

Stability analysis of a flow studies the transition of a simple laminar base flow to a bifurcated complex system of flow, or later to a turbulent flow. Hydrodynamic stability analysis deals with the transition region of any flow. Linear bi-global stability analysis of eccentric Taylor-Couette(TC) flow is slightly complicated compared to the simple TC system, for the eccentric system is hard to solve in a traditional radial coordinate system. Simple TC system can be solved using a pseudo - parallel flow assumption and solving the Orr-Squire system of governing equations, while eccentric TC flow is completely non-parallel and complex. The work around authors employed here is to use a bipolar coordinate system for representing the governing equations. Base flow is solved using a Finite Volume Method to numerically approximate the solution of governing Navier Stokes equations and then interpolated to the points required in the bipolar coordinates to solve for stability. Chebyshev-Fourier collocation spectral method is used to solve for the governing stability equations, since the angular flow is to be periodic. The biglobal stability analysis reveals modes of instability in the plane of rotation of the inner cylinder. The axial coordinate is assumed to be periodic. The stability code which is validated with the simple TC system, revealed that the eccentric system is stable for higher Reynolds number than the concentric system. It also revealed formation of Taylor vortices as its first instability.