Linear stability of a nonorthogonal axisymmetric stagnation flow on a rotating cylinder

The present analysis deals with the onset of instability in an axisymmetric stagnation flow obliquely impinging on a uniformly rotating circular cylinder. The basic flow is described by an exact solution of the Navier-Stokes equations, discovered by Weidmann and Putkaradze [Eur. J. Mech. B/Fluids 22...

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Bibliographic Details
Published in:Physics of fluids (1994) 2006-12, Vol.18 (12), p.1-13
Main Authors: Amaouche, Mustapha, Bouda, Faïçal Nait, Sadat, Hamou
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Laminar flows
Mechanics
Physics
Stability of laminar flows
Thermics
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Summary:The present analysis deals with the onset of instability in an axisymmetric stagnation flow obliquely impinging on a uniformly rotating circular cylinder. The basic flow is described by an exact solution of the Navier-Stokes equations, discovered by Weidmann and Putkaradze [Eur. J. Mech. B/Fluids 22, 123 (2003)]. An eigenvalue problem for the linear stability is formulated, regardless of the free stream obliqueness, and then solved numerically by means of a collocation method using Laguerre’s polynomials. It is established that the basic stagnation flow is stable for sufficiently high Reynolds numbers. This is in conformity with the unconditional linear stability of two-dimensional Hiemenz stagnation flow. Instability occurs for Reynolds numbers smaller than some threshold value that increases with the rotation rate of the cylinder. At criticality, the flow undergoes a Hopf bifurcation, leading then to an oscillatory secondary motion.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.2403179