Investigation of the Taylor-Couette and Dean Instability problems using Chebyshev Spectral Method

In fluid dynamics, the Taylor–Couette flow consists of a viscous fluid confined in the gap between two rotating cylinders. Furthermore, when the liquid is allowed toflow in the annular space of two rotating cylinders along with the application of a pressure gradient, then a flow called Taylor–Dean flow arises. For low angularvelocities, it’s measured by the Reynolds number Re, the flow is steady and purely azimuthal centrifugal. Inthis work, instability of Newtonian fluids is investigated in Taylor–Couette and Dean flow when the gap size is small compared to the cylinders radii. This instability isdue to the destabilizing effect of the centrifugal force, and there is a competition between this effect and the stabilizing effect of viscous drag force. An eigenvalueproblem was obtained for this instability which was solved numerically using the spectral method. For Taylor-Couette instability the plot of wave numberversus Taylor number shows that in each angular velocity ratio (μ) there is a specific Taylor number,called Tc that flow remain always stable for TTaylor-Couette and it was found a critical Dean number that flow remains stable for Λ < Λc.

کلیدواژه ها:

Taylor-Couette ، Dean Instability ، Chebyshev Spectral Method