Turbulence in a localized puff in a pipe

A. Yakhot, Y. Feldman, D. Moxey, S. J. Sherwin, G. E. Karniadakis

Flow Turbul. Combust., vol. 103, pp. 1–24 (2019)

@article{yakhot-2019,
  title = {Turbulence in a localized puff in a pipe},
  author = {Yakhot, A. and Feldman, Y. and Moxey, D. and Sherwin, S. J. and Karniadakis, G. E.},
  journal = ftc,
  volume = {103},
  number = {1},
  pages = {1--24},
  year = {2019},
  url = {https://davidmoxey.uk/assets/pubs/2018-puff-turb.pdf},
  doi = {10.1007/s10494-018-0002-8},
  abstract = {We have performed direct numerical simulations of a spatio-temporally intermittent flow in a pipe for $Re_m = 2250$. From previous experiments and simulations of pipe flow, this value has been estimated as a threshold when the average speeds of upstream and downstream fronts of a puff are identical. We investigated the structure of an individual puff by considering three-dimensional snapshots over a long time period. To assimilate the velocity data, we applied a conditional sampling based on the location of the maximum en- ergy of the transverse (turbulent) motion. Specifically, at each time instance, we followed a turbulent puff by a three-dimensional moving window centered at that location. We collected a snapshot-ensemble (10000 time instances, snap- shots) of the velocity fields acquired over $T = 2000D/U$ time interval inside the moving window. The cross-plane velocity field inside the puff showed the dynamics of a developing turbulence. In particular, the analysis of the cross- plane radial motion yielded the illustration of the production of turbulent kinetic energy directly from the mean flow. A snapshot-ensemble averaging over 10000 snapshots revealed azimuthally arranged large-scale (coherent) structures indicating near-wall sweep and ejection activity. The localized puff is about 15-17 pipe diameters long and the flow regime upstream of its upstream edge and downstream of its leading edge is almost laminar. In the near-wall region, despite the low Reynolds number, the turbulence statistics, in particular, the distribution of turbulence intensities, Reynolds shear stress, skewness and flatness factors, become similar to a fully-developed turbulent pipe flow in the vicinity of the puff upstream edge. In the puff core, the velocity profile becomes flat and logarithmic. It is shown that this ``fully-developed turbulent flash'' is very narrow being about two pipe diameters long.}
}

Close to the transition to turbulence, flow in a pipe carries localised turbulent patches called puffs that travel through otherwise laminar fluid. This paper follows a single puff in direct numerical simulation at a Reynolds number of 2250, using a three-dimensional window that moves with the point of maximum transverse energy to collect 10,000 snapshots. The puff turns out to be 15 to 17 pipe diameters long, and near the wall its turbulence statistics come to resemble those of fully developed turbulent pipe flow despite the low Reynolds number.