Chaotic mixing in a helix-like pipe with periodic variations in curvature and torsion

Chaotic motion of fluid particles due to a steady viscous flow in a helix-like circular pipe caused by an axial pressure gradient, and the mixing efficiency of this flow are numerically examined here. The pipe is wound around a circular or elliptic cylinder with a constant pitch so that the curvature kappa and torsion tau of the centerline of this pipe vary continuously and periodically. If both kappa and tau are small and slowly varying, the cross-sectional motion of fluid particles is expected to be approximately governed by the sum of Dean's flow and the flow of rigid rotation. From Poincare sections and the values of an index of the extent of mixing, it is found that there is an intermediate range of Reynolds number Re of flow within which chaotic regions in Poincare sections are large and mixing efficiency over a short time is high. Moreover, larger chaotic regions and higher mixing efficiency are observed for pipes wound around a circular cylinder of smaller radius and for pipes wound around a thinner elliptic cylinder. These results can be explained by the variation in characteristic ratio lambda = 12 tau/(kappa Re) in one period.