Effect of the Womersley number on transition to turbulence in pipe flow: An experimental study

Abstract

The mechanisms driving the transition to turbulence in pulsatile flows are not well understood. Prior studies in this domain have noted the dynamics of this flow regime to depend on the mean Reynolds number, pulsation frequency (i.e., Womersley number), and inflow pulsatile waveform shape. Conflicting findings, particularly regarding the role of the Womersley number on the critical Reynolds number and the development of turbulence, have been reported. The discord has primarily been observed for flows, with Womersley numbers ranging from 4 to 12. Hence, in this work, we use particle image velocimetry to explore the effects of the Womersley number within this 4–12 range on the dynamics of the pulsatile transition. Eighteen test cases were captured using six mean Reynolds numbers (range 800–4200) and five Womersley numbers. Turbulent kinetic energy, turbulence intensity (TI), and phase lag were computed. Our results indicated that the critical Reynolds number was roughly independent of the Womersley number. At high Womersley numbers, the TI trend maintained lower pulsatility, and the flow was observed to mimic a steady transitional flow regime. A plateau of the TI-velocity and TI-acceleration phase lag was observed at a Womersley number of 8, highlighting that this may be the critical value where further increases to the Womersley number do not alter the transition dynamics. Furthermore, this suggests that the phase lag may provide a universal indicator of the specific influence of the Womersley number on transition for a given flow. Overall, these findings elucidate critical details regarding the role of the Womersley number in the transition to turbulence.