Laminar similarities between accelerating and decelerating turbulent flows

Abstract

An experimental study of a pipe flow ramping monotonically between two turbulent states has been undertaken. Ensemble-averaged mean and turbulent flow quantities obtained from two-component particle image velocimetry and hot-film anemometry measurements have been presented. It is shown that the time-developments of the mean and turbulence quantities in accelerating and decelerating flows are similar during an initial stage following the transients. Specifically, the mean perturbation velocity (defined as the surplus/deficit from the initial value) can be described using self-similar expressions. The duration of this initial stage is shown to be a decreasing function of the dimensionless parameter δ=ν/uτ02(1/Ub0)dUb/dt. Data from studies of linearly accelerating and decelerating flows as well as impulsively accelerating and decelerating flows have been used to validate the results, covering four orders of magnitude of δ. The highest initial Reynolds number investigated in this study (35,700) is, however, relatively low thus requiring further studies at high Reynolds numbers to assure the universality of the results. We have also shown that the time-developments of the mean and turbulent quantities between an accelerating and a decelerating flow loose their similarity as the transient proceeds beyond the initial stage. The departure was explained by the time-evolvement of the production of turbulence kinetic energy, which exhibit differences between the two types of transients.