3D CFD study of hydrodynamics and mass transfer phenomena for spiral wound membrane submerged-type feed spacer with different node geometries and sizes

Modification of the spacer geometry is a promising approach to increase the efficiency of reverse osmosis (RO) spiral wound membrane modules. Column nodes and spherical nodes are considered in this three-dimensional computational fluid dynamic (CFD) study to evaluate the hydrodynamic and mass transfer performance of submerged spacers with different node geometries and sizes. Small-scale CFD analysis results reveal that the column node has better mass transfer performance than the spherical node geometry because column nodes divert more flow to the filaments, leading to higher local velocity at the region between the filament and wall. Furthermore, when the dimensionless node diameter ratio of the column nodes increases from 0.3 to 1.2, Sherwood number and wall shear increase by 25% and 8% respectively at the expense of higher global friction factor (44%). A sea water RO full-scale analysis revealed that column node spacers yield higher average flux than spherical nodes and conventional spacers at high feed inlet velocity (> 0.1 m/s), because the mixing effects by the spacer that improve mass transfer are more prominent

Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays

The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators of union, intersection, and difference, i.e., any CSG tree. The result is obtained in three steps: first, by computing an independent set of generators for the d-space partition induced by the input; then, by reducing the solid expression to an equivalent logical formula between Boolean terms made by zeros and ones; and, finally, by evaluating this expression using bitwise operators. This method is implemented in Julia using sparse arrays. The computational evaluation of every possible solid expression, usually denoted as CSG (Constructive Solid Geometry), is reduced to an equivalent logical expression of a finite set algebra over the cells of a space partition, and solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig