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Prediction of the critical Reynolds number for flow past a circular cylinder. (English) Zbl 1119.76031
Summary: We attempt to estimate the critical Reynolds number, \(Re_{c}\), for the first wake instability of the wake associated with a flow past a circular cylinder. Linear stability analysis and direct time integration of the governing equations for incompressible flows are carried out via a stabilized finite element formulation. The generalized eigenvalue problem resulting from the finite element discretization of the equations from linearized stability analysis is solved using a subspace iteration method to get the most unstable eigenmode. The results from the two methods are in good agreement. We investigate the effect of spatial resolution and location of computational boundaries. It is found that, for high blockage (ratio of the diameter of cylinder to the lateral width of domain), \(Re_{c}\) first decreases and then increases with increase in blockage. It is also observed that the Strouhal number at \(Re_{c}\) is quite sensitive to the blockage. This might possibly explain the scatter in the data from various researchers in the past.

76E99 Hydrodynamic stability
76M10 Finite element methods applied to problems in fluid mechanics
76D25 Wakes and jets
Full Text: DOI
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