Using coordinate transformation of Navier-Stokes equations to solve flow in multiple helical geometries

Recent research on small amplitude helical pipes for use as bypass grafts and arteriovenous shunts, suggests that mixing may help prevent occlusion by thrombosis. It is proposed here that joining together two helical geometries, of different helical radii, will enhance mixing, with only a small increase in pressure loss. To determine the velocity field, a coordinate transformation of the Navier-Stokes equations is used, which is then solved using a 2-D high-order mesh combined with a Fourier decomposition in the periodic direction. The results show that the velocity fields in each component geometry differ strongly from the corresponding solution for a single helical geometry. The results suggest that, although the mixing behaviour will be weaker than an idealised prediction indicates, it will be improved from that generated in a single helical geometry.