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# Improved Mass Transfer Performance of Membrane units in a Toroidal Helical Pipe—reduction of concentration polarization by secondary flows

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## Abstract

We evaluate a Toroidal Helical Pipe (THP) for the extent of process intensification that it can offer over an equivalent length of straight pipe by providing continuous curvature changes resulting in complex secondary flows in a compact space. The present study is a radical departure from traditional curved and helical tubes with constant curvatures as they often lead to a fully-developed state. The THP results in a continuously varying curvature. Here we examine the application of THP for membrane transport, where reducing the concentration polarization is a challenge. We build the geometry from a 3d space curve represented by C(t;R,r,n)=[(R+r·cosnt)·cost,(R+r·cosnt)·sint,r·sinnt], where R is the radius of the torus, r is the radius of the pipe, and n is the number of turns of the helical pipe around the torus. Although this enables a design optimization study over the geometric parameter space (R,r,n), we restrict our study to the following values C(t;5,1.2,7).The computational model is used to study solutions for a Reynolds number of up to Re=100 and a Peclet number of Pe=6×104. We demonstrate a significant reduction in the concentration polarization aided by the secondary flows with increasing Re. The permeate flow increased by 33% at Re=100.

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