Dean vortices applied to membrane process: Part II: Numerical approach

This work is devoted to the numerical study of the flow inside helical hollow fibers. For a wide range of Reynolds numbers and of helix shapes, corresponding to woven or non-woven, permeable or non-permeable fibers, the corresponding three-dimensional velocity field is calculated in order to study the velocity profiles and the local wall shear stress. The influence of permeation is not qualitatively marked within the ranges of conditions that reproduce the classical experimental ultrafiltration conditions. The permeate flux density depends on the permeability of the membrane and is constant on the perimeter of a cross-section of the tube. For all the permeability situations considered, the Dean flow depends on three parameters: the Reynolds number, the curvature and the helix torsion. The effect of each of these parameters depends largely on the relative values of the two others. The Dean number makes it possible to predict the mean shear stress, as well as its distribution along the perimeter of a cross-section. For woven fibers, as their diameter is small, the pitch has a significant influence on the curvature.