The Stability of Pipe Entrance Flows Subjected to Axisymmetric Disturbances

Abstract

This paper reexamines an important unresolved problem in fluid mechanics—the discrepancy between measurements and predictions of stability in pipe entrance flows. Whereas measured critical Reynolds numbers are relatively insensitive to velocity profile shape in the streamwise direction, the theoretical results indicate a rapid increase, both as the equilibrium profile is approached, and toward the inlet. The current work uses the displacement thickness based Reynolds number as a rational basis on which to compare new stability predictions obtained by means of the Q-Z algorithm, with existing theoretical results. Although the present data are shown to be the only that are consistent with the classical parallel boundary layer limit towards the inlet, they still deviate increasingly with axial distance from the only available experimental results. By examining pipe inlet stability data in relation to boundary layer measurements and predictions, the work effectively questions the commonly held belief that streamwise variations of flow alone are responsible for these deviations, suggesting that the finite amplitude nature of the applied disturbances is the most likely cause.