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