Pulsating pipe flow with large-amplitude oscillations in the very high frequency regime. Part 1. Time-averaged analysis

Abstract

AbstractThis paper numerically investigates the effects of a harmonic volume forcing of prescribed frequency on the turbulent pipe flow at a Reynolds number, based on bulk velocity and pipe diameter, of 5900. The thickness of the Stokes layer, resulting from the oscillatory flow component, is a small fraction of the pipe radius and therefore the associated vorticity is confined within a few wall units. The harmonic forcing term is prescribed so that the ratio of the oscillating to the mean bulk velocity ($\ensuremath{\beta} $) ranges between 1 and 10.6. In all cases the oscillatory flow obeys the Stokes analytical velocity distribution while remarkable changes in the current component are observed. At intermediate values $\ensuremath{\beta} = 5$, a relaminarization process occurs, while for $\ensuremath{\beta} = 10. 6$, turbulence is affected so much by the harmonic forcing that the near-wall coherent structures, although not fully suppressed, are substantially weakened. The present study focuses on the analysis of the time- and space-averaged statistics of the first- and second-order moments, vorticity fluctuations and Reynolds stress budgets. Since the flow is unsteady not only locally but also in its space-averaged dynamics, it can be analysed using phase-averaged and time-averaged statistics. While the former gives information about the statistics of the fluctuations about the mean, the latter, postponed to a subsequent paper, shows how the mean is affected by the fluctuations. Clearly, the two phenomena are connected and both of them deserve investigation.