Pulsating turbulent pipe flow in the current dominated regime at high and very-high frequencies

Highlights: • High frequency pulsating flow can be decomposed in a mean and an oscillatory part. • The turbulence statistics of the oscillatory part depend only on the characteristics of the pulsation. • An effective scaling factor for the turbulence statistics is the ratio of the frequency parameter to the amplitude. • There is no clear distinction between the high and very high frequency regimes. - Abstract: The paper presents Direct Numerical Simulations of sinusoidal pulsating turbulent flow, at low bulk Reynolds numbers, with high frequency, in a straight pipe. Our objective is to study pulsating flow considering it as the superposition of a temporal unsteadiness on a mean current, and from this viewpoint, to decompose the flow in a mean and an oscillating part. Firstly, we examine the time-averaged statistics, which show that the parent flow retains its properties. Then, we analyze the oscillating part of the flow, and confirm the notion that for rapidly pulsating flow, the amplitude of the streamwise velocity and the phase lag at different radial locations follow the solution of the laminar Stokes problem. In addition, we find that the modulation of the turbulent fluctuations follows approximately the sinusoidal form of the imposed pulsation, and that the ratio of the frequency parameter to the amplitude of the streamwise velocity can be used as a scaling factor. We investigate the effects of the amplitude and the frequency of the imposed unsteadiness on the modulation of the time-averaged properties and the turbulence statistics, through a systematic analysis. Finally, we examine the time evolution of the mean velocity and the turbulent fluctuations. These results indicate that a lower limit for the high frequency regime can be identified, based on the level of conformity of the phase-averaged profiles on their steady-state counterparts. For very high frequencies, we find that that the flow behavior does not change, indicating the absence of an upper limit for the high frequency regime.