Unstable Regions in Impulsively Started Pipe Entrance Flows Subjected to Infinitesimal Axisymmetric Disturbances

This investigation presents computed base flow and stability data (axisymmetric disturbances) for impulsively started pipe entrance flows, and shows that at any given time, the displacement thickness (or any other flow variable) variation with axial distance is given by a varying portion which is accurately described by a steady, spatially developing flow, followed by a constant portion, described by the impulsively started parallel system. At the transition between these two systems is a small portion which is described by neither model. Arising from the inference that the latter region is sufficiently small to be neglected, variations in time and space of unstable regions in impulsively started pipe entrance flows were established, showing that (i) such flows are are unconditionally stable to infinitesimal axisymmetric disturbances for a Reynolds number of less than 23 350; (ii) for 38 770 > Re > 23 350, possible instability is confined to a maximum of 3.7% of the entire steady pipe entrance region; and (iii) for Re > 38 770, unstable regions may occur for finite time durations, over the entire length of the pipe.