Downstream decay of fully developed Dean flow

Jesse T. Ault, Kevin K. Chen, Howard A. Stone

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Direct numerical simulations were used to investigate the downstream decay of fully developed flow in a 180° curved pipe that exits into a straight outlet. The flow is studied for a range of Reynolds numbers and pipe-to-curvature radius ratios. Velocity, pressure and vorticity fields are calculated to visualize the downstream decay process. Transition 'decay' lengths are calculated using the norm of the velocity perturbation from the Hagen-Poiseuille velocity profile, the wall-averaged shear stress, the integral of the magnitude of the vorticity, and the maximum value of the Q-criterion on a cross-section. Transition lengths to the fully developed Poiseuille distribution are found to have a linear dependence on the Reynolds number with no noticeable dependence on the pipe-to-curvature radius ratio, despite the flow's dependence on both parameters. This linear dependence of Reynolds number on the transition length is explained by linearizing the Navier-Stokes equations about the Poiseuille flow, using the form of the fully developed Dean flow as an initial condition, and using appropriate scaling arguments. We extend our results by comparing this flow recovery downstream of a curved pipe to the flow recovery in the downstream outlets of a T-junction flow. Specifically, we compare the transition lengths between these flows and document how the transition lengths depend on the Reynolds number.

Original languageEnglish (US)
Pages (from-to)219-244
Number of pages26
JournalJournal of Fluid Mechanics
StatePublished - Jul 15 2015

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • low-Reynolds-number flows


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