An experimental investigation of the stability of Poiseuille flow

Abstract

An axially symmetric laminar flow of air was established in a long smooth pipe. This flow was steady up to Reynolds numbers of about 20,000, the capacity of the system. Small, nearly axially, symmetric disturbances were superimposed by longitudinally oscillating a thin sleeve adjacent to the inner wall of the pipe. Hot-wire anemometer measurements consisting of radial and longitudinal traverses were made downstream of the sleeve. These measurements indicated that within the Reynolds number range investigated (up to 13,000), the flow is stable to small disturbances. In general, the radial distribution of disturbance amplitudes was not independent of distance downstream; while the disturbances, as generated, exhibited imperfect axial symmetry, the non-symmetric part decayed more rapidly than the symmetric part. Results were interpreted in such a way that rates of propagation and rates of decay of the disturbances could be compared with those given by a recent theoretical stability analysis. It was found that the rates of decay are predicted fairly satisfactorily by the theory; however, the rates of propagation are not. In addition, it was found that transition to turbulent flow occurs whenever the amplitude of the disturbance exceeds a threshold value which decreases with increasing Reynolds number. Due to the departures from axial symmetry in the amplitude of the disturbance, it was not possible to obtain a quantitative measure of the threshold. A mathematical idealization of the disturbances, believed to be more akin to experimental perturbations than the classical model used in small-perturbation analyses, is proposed.