Developing Lengths in Woven and Helical Tubes with Dean Vortices Flows

Abstract

Coiling membranes help to create in a flow Dean vortices which enhance flux permeation and bring improvement to membrane filtration processes. The Dean number enables prediction of the appearance of those vortices. As it increases, a secondary flow appears with one pair of vortices. However, this flow profile needs a certain length to be fully developed. For membrane processes, it is useful to know this developing length so one can calculate the exact membrane area under such Dean shear stress. Developing angles or lengths were already simulated for a parabolic and a uniform inlet flow for a torus. In this study, we determined numerically the developing length for different kinds of tori and for woven or helical tubes. The simulations featured parameters of wide ranges of validity: internal diameter (0.25–1 mm), coil diameter (4–32 mm), Reynolds number (0–400) and pitch (2–32 mm) for the helical shape.