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Linear Stability Analysis of Taylor-Couette Flow with and without Viscous Heating

Mayank Thummar, Sagar Mehta


This paper presents linear stability analysis of the incompressible viscous flow between the two concentric counter rotating cylinders. The parallel flow assumption is applied; hence the mean flow is the function of radial coordinate only. The main objective of this study is to explore the effect of the viscous heating, Nahme number and radius ratio (Ratio of inner to outer cylinder radius, η) on the stability characteristics of Taylor-Couette flow. Linearized Navier-stokes (LNS) equations are derived for 3-D disturbance flow quantities by standard procedure. The disturbance energy equation is also coupled to the LNS equation. Chebyshev spectral collocation method is used to discretize the Linearized Navier-Stokes equations. The governing equations along with appropriate boundary conditions form a general eigen values problem. The QZ algorithm is used to solve the full eigen value problem. The full spectrum of eigen values and corresponding eigen vectors are computed. Local temporal modes are computed for the different Reynolds number and radius ratio. It has been found that the critical Reynolds number decreases without considering the effect of viscous heating for the radius ratio (η) in the range of 0.2 to 0.6, and it is nearly constant in the range of η from 0.6 to 0.8 and beyond the 0.8, it increases. Critical Re decreases due to viscous heating effect and flow become unstable at lower Reynolds number. The effect of Nahme number is also to reduce Critical Reynolds number.

Keywords: Stability, viscous heating, critical Re, radius ratio, Taylor-Couette, Nahme-number

Cite this Article

Mayank Thummar, Sagar Mehta. Linear Stability Analysis of Taylor-Couette Flow with and without Viscous Heating. Recent Trends in Fluid Mechanics. 2017; 4(2): 15–22p.

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