Mixing through stirring of steady flow in small amplitude helical tubes

A N Cookson, D J Doorly, S J Sherwin

Research output: Contribution to journalArticlepeer-review

47 Citations (SciVal)


In this paper we numerically simulate flow in a helical tube for physiological conditions using a co-ordinate mapping of the Navier-Stokes equations. Helical geometries have been proposed for use as bypass grafts, arterial stents and as an idealized model for the out-of-plane curvature of arteries. Small amplitude helical tubes are also currently being investigated for possible application as A-V shunts, where preliminary in vivo tests suggest a possibly lower risk of thrombotic occlusion. In-plane mixing induced by the geometry is hypothesized to be an important mechanism. In this work, we focus mainly on a Reynolds number of 250 and investigate both the flow structure and the in-plane mixing in helical geometries with fixed pitch of 6 tube diameters (D), and centerline helical radius ranging from 0.1 D to 0.5 D. High-order particle tracking, and an information entropy measure is used to analyze the in-plane mixing. A combination of translational and rotational reference frames are shown to explain the apparent discrepancy between flow field and particle trajectories, whereby particle paths display a pattern characteristic of a double vortex, though the flow field reveals only a single dominant vortex. A radius of 0.25 D is found to provide the best trade-off between mixing and pressure loss, with little increase in mixing above R=0.25 D, whereas pressure continues to increase linearly.

Original languageEnglish
Pages (from-to)710-721
Number of pages12
JournalAnnals of Biomedical Engineering
Issue number4
Publication statusPublished - Apr 2009


  • Animals
  • Computer Simulation
  • Entropy
  • Models, Biological
  • Models, Theoretical
  • Particle Size
  • Physical Phenomena
  • Rotation
  • Journal Article
  • Research Support, Non-U.S. Gov't


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