Study of a toroidal-helical pipe as an innovative static mixer in laminar flows

Abstract

In this paper we present the design of a novel, passive mixer, to enhance mixing and residence time distribution for promoting transport and reaction mechanisms in such devices. The goal is to understand and optimize the flow patterns for enhancing mixing in laminar flows through toroidal helical pipes, inspired by the coiled flow inverter (CFI) (Saxena and Nigam, 1984). A toroidal helix is a smooth analytical curve winding around a torus. It is characterized by three parameters: the radius of the torus' centerline, the radius of the torus’ cross-section, and the number of turns it winds around the torus. Unlike the torus or the straight helix which have constant curvatures, the toroidal helix has a spatially oscillating curvature. We found that this causes the otherwise separated pair of Dean vortices to couple together, periodically re-orient, shrink and grow within each turn of the pipe. The resultant complex streamlines span the entire cross-section and enhances mixing via advective means. By constraining the total pipe length, a meaningful comparison of mixing efficiency within a given volume of pipe can be assessed as the torus’s cross-section radius and the number of helix turns are systematically varied. Reynolds number of up to 400 is explored with the number of turns of 3, 5, 7 and 8. The optimization study shows that the best mixing performance is achieved using a moderate number of turns. Apart from flow pattern and mixing efficiency, we also studied the pressure drop to monitor increased energy consumption and residence time distribution of the flow to monitor degree of mixing.