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Turbulence in a Localized Puff in a Pipe

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Abstract

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.

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Notes

  1. Thus, when we say “at the moving window trailing edge S01,” it also implies “slightly downstream of the upstream edge of the puff.”

  2. “Low-speed” (w < 0) and “high-speed” (w > 0) are usually used as relative terms, and refer to deviations from the mean streamwise velocity value at that location.

  3. In this study, we take into account that the near-wall ejection and sweeping correlate and are spatially close. Therefore, the computed range of \(|\text {R}_{u_{r},u_{r}}|>0.2\) leads us to consider these data as well correlated.

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Acknowledgements

One of the authors (AY) would like to thank Dr. N. Nikitin (Moscow State University) for providing some DNS channel data and helpful comments.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ben-Gurion University, Beersheva, 84105, Israel

    Alexander Yakhot & Yuri Feldman

  2. College of Engineering Mathematics and Physical Sciences, University of Exeter, N Park Rd, Exeter, EX4 4QF, UK

    David Moxey

  3. Department of Aeronautics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK

    Spencer Sherwin

  4. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    George Em Karniadakis

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  1. Alexander Yakhot
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  2. Yuri Feldman
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  3. David Moxey
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  4. Spencer Sherwin
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  5. George Em Karniadakis
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Correspondence to Alexander Yakhot.

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Yakhot, A., Feldman, Y., Moxey, D. et al. Turbulence in a Localized Puff in a Pipe. Flow Turbulence Combust 103, 1–24 (2019). https://doi.org/10.1007/s10494-018-0002-8

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