Turbulence in a Localized Puff in a Pipe
We have performed direct numerical simulations of a spatio-temporally intermittent flow in a pipe for Rem = 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 (Barkley et al., Nature 526, 550–553, 2015; Barkley et al., 2015). 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 energy 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, snapshots) 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.
KeywordsTransition to turbulence Puff Pipe flow
One of the authors (AY) would like to thank Dr. N. Nikitin (Moscow State University) for providing some DNS channel data and helpful comments.
Compliance with Ethical Standards
Conflict of interests
The authors declare that they have no conflict of interest.
- 2.Barkley, D., Song, B., Mukund, V., Lemoult, G., Avila, M., Hof, B.: The rise of fully turbulent flow. Available from: arXiv:1510.09143.pdf(2015)
- 18.Moxey, D.: Spatio-temporal dynamics in pipe flow. PhD thesis, University of Warwick (2011)Google Scholar
- 19.Moser, R. D., Moin, P.: Direct numerical simulation of curved turbulent channel flow. NASA Tech. Memo. 85974, 84–87 (1984)Google Scholar