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Volume 4,     Number 4,     Fall 1996

 

STEADY, UNSTEADY AND LINEAR STABILITY
OF FLOW PAST AN ELLIPTIC CYLINDER
S.J.D. D'ALESSIO

Abstract. Discussed in thin work is the two-dimensional steady state and unsteady flow of a viscous incompressible fluid past an inclined elliptic cylinder. Numerical solutions to the Navier-Stokes equations have been obtained for moderate Reynolds numbers, R, up to 100 and for various inclinations, α. It is observed that for low R the limiting unsteady problem agrees well with the steady state results while for 20 < R < 30 the unsteady flow succumbs to vortex shedding. Good agreement in the steady state results is found with existing results for R = 40. Also included is a linear stability analysis. The minimum critical Reynolds number at which the flow becomes unstable due to asymmetric disturbances has been estimated to lie in the range 35 < Rc < 40 and to occur for an inclination in the interval 40 < αc < 50. Similarly, for the circular cylinder Rc was estimated to be between 100 <Rc < 110.

 

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