Recent research on small amplitude helical pipes for use as bypass grafts and arterio- venous shunts suggest that in-plane mixing induced by the geometry may help pre- vent occlusion by thrombosis. In this thesis, a coordinate transformation of the Navier-Stokes equations is solved within a spectral/hp element framework to study the flow field and mixing behaviour of small-amplitude helical pipes. An apparent discrepancy between the flow field and particle trajectories is observed, whereby particle paths display a pattern characteristic of a double vortex, though the flow field reveals only a single dominant vortex. It is shown that a combination of trans- lational and rotational reference frames changes resolves this discrepancy.

It is then proposed that joining together two helical geometries, of differing helical radii, will enhance mixing, through the phenomenon of ‘streamline crossing’. An idealised prediction of the mixing is obtained by concatenating the velocity field solutions from the respective single helical geometries. The mixing is examined using Poincar ́e sections, residence time data and information entropy. The flow is then solved for those combined geometries showing the most improvement in mixing, with a 70% increase in mixing efficiency achieved, with only a small increase in pressure loss. It is found that although the true velocity fields vary significantly from the prediction, the overall mixing behaviour is captured, allowing the use of the idealised prediction for guiding future designs of combined geometries.