Prediction of the critical Reynolds number for flow past a circular cylinder

Abstract

In this paper we attempt to estimate the value of critical Reynolds number, Re_c, for the first wake instability of the wake associated with the flow past a circular cylinder. Linear stability analysis (LSA) and direct time integration (DTI) 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 (SI) method to get the most unstable eigenmode. The results from the two methods are in good agreement. The effect of spatial resolution and location of computational boundaries is investigated. 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.