Onset of global instability in the flow past a circular cylinder cascade

The effect of blockage on the onset of instability in the two-dimensional uniform flow past a cascade of cylinders is investigated. The same techniques as those described in Gajjar & Azzam (J. Fluid Mech., vol. 520, 2004, p. 51) are used to tackle the generalized eigenvalue problem arising from a global stability analysis of the linearized disturbance equations. Results have been obtained for the various mode classes, and our results show that for the odd–even modes, which correspond to anti-phase oscillatory motion about the midplane between the cylinders and are the modes most extensively studied in the literature, the effect of blockage has a marginal influence on the critical Reynolds numbers for instability. This is in sharp contrast to results cited in many studies with a fully developed inlet flow past a cylinder placed between confining walls. We are also able to find other unstable modes and in particular for low blockage ratios, the odd–odd modes which correspond to the in-phase oscillatory motion about the midplane between the cylinders are the first to become unstable as compared with the odd–even modes, and with much lower frequencies.