Authors : M. Boubekri and M. Afrid
Abstract: We consider the numerical simulation of the two-dimensional viscous flow over a solid ellipse with an aspect ratio equal 3.5. Sufficiently far from the ellipse, the flow is assured potential. The flow is modelled by the two dimensional partial differential equations of conservation of masse and moment, using elliptic coordinates. The finite volume method is used to discritize the model equations. The numerical solutions revealed that the flow over the ellipse is steady with zero vortex up to Re = 40. For Reynolds numbers between 50 and 190, the flow is steady with two vortices in the wake. For Re = 210 the flow becomes unstable with harmonic oscillations: The two vortices are alternate in the time with a Strouhal number equal to 0.2075. For the Reynolds number between 220 and 280 the vortices are detached one after other. The spectral analysis of the discrete time variation of the flow velocity at a point within the upper vortex shows that the dominant oscillations frequency is f = 0.2748.
M. Boubekri and M. Afrid , 2008. Some Modes of the Incompressible Flow on an Elliptic Cylinder at Low Reynolds Number. Journal of Engineering and Applied Sciences, 3: 94-99.