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A streamwise-constant model of turbulent pipe flow

Bourguignon, Jean-Loup and McKeon, Beverley J. (2011) A streamwise-constant model of turbulent pipe flow. Physics of Fluids, 23 (9). Art. no. 095111. ISSN 1070-6631.

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A streamwise-constant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. The model is subject to two different types of forcing: a simple forcing of the axial momentum equation via a deterministic form for the streamfunction and a stochastic forcing of the streamfunction equation. Using a single forced momentum balance equation, we show that the shape of the velocity profile is robust to changes in the forcing profile and that both linear non-normal and nonlinear effects are required to capture the change in mean flow associated with transition to turbulence. The particularly simple form of the model allows for the study of the momentum transfer directly by inspection of the equations. The distribution of the high- and low-speed streaks over the cross-section of the pipe produced by our model is remarkably similar to one observed in the velocity field near the trailing edge of the puff structures present in pipe flow transition. Under stochastic forcing, the model exhibits a quasi-periodic self-sustaining cycle characterized by the creation and subsequent decay of “streamwise-constant puffs,” so-called due to the good agreement between the temporal evolution of their velocity field and the projection of the velocity field associated with three-dimensional puffs in a frame of reference moving at the bulk velocity. We establish that the flow dynamics are relatively insensitive to the regeneration mechanisms invoked to produce near-wall streamwise vortices, such that using small, unstructured background disturbances to regenerate the streamwise vortices in place of the natural feedback from the flow is sufficient to capture the formation of the high- and low-speed streaks and their segregation leading to the blunting of the velocity profile characteristic of turbulent pipe flow. We propose a “quasi self-sustaining process” to describe these mechanisms.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
McKeon, Beverley J.0000-0003-4220-1583
Additional Information:© 2011 American Institute of Physics. Received 4 June 2011; accepted 16 August 2011; published online 29 September 2011. The authors gratefully acknowledge the support of the AFOSR Grant No. FA 9550-09-1-0701 (program manager John Schmisseur).
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA 9550-09-1-0701
Subject Keywords:flow simulation; laminar to turbulent transitions; pipe flow; turbulence; vortices
Issue or Number:9
Classification Code:PACS:; 47.32.C-; 47.60.Dx; 47.27.eb; 47.27.Cn; 47.11.-j
Record Number:CaltechAUTHORS:20111115-094643184
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Official Citation:A streamwise-constant model of turbulent pipe flow Jean-Loup Bourguignon and Beverley J. McKeon, Phys. Fluids 23, 095111 (2011), DOI:10.1063/1.3640081
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27781
Deposited By: Jason Perez
Deposited On:15 Nov 2011 18:53
Last Modified:03 Oct 2019 03:26

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