A numerical and experimental study of mass transfer in spacer-filled channels: Effects of spacer geometrical characteristics and Schmidt number

A systematic study is presented on the effect of both Reynolds (Re) and Schmidt (Sc) numbers on Sherwood (Sh) number, for narrow channels with spacers, closely simulating conditions of feed-side channels in spiral-wound modules. Results of direct numerical simulations performed for the three-dimensional geometries resulting from non-woven cylindrical filament (net-type) spacers show the significant influence of spacer geometry on local Sh distributions. These distributions exhibit a tendency to be displaced towards lower values for more sparse spacer geometries, and towards higher values as the angle between crossing filaments is increased. Additionally, the distribution of the local time-averaged mass transfer coefficients is generally similar to the corresponding distribution of shear stresses at the channel walls, with a tendency to exhibit closer similarity with increasing Sc, as one would expect. To validate the results of numerical simulation, a significant amount of mass transfer data is reported for nine different prototype spacer geometries, plus a common commercial spacer, and three Sc numbers in each case. Correlations of average Sh are obtained for each geometry, in terms of Re and Sc numbers; the exponent of Sh dependence on Sc is near 0.4, as is also obtained from the numerical simulations. Moreover, in agreement with the numerical results, the experimental data reveal a similar trend in the dependence of the average Sh number on spacer geometrical characteristics, namely decreasing with increasing ratio L/D (of cell side L over filament diameter D) and increasing with the filaments crossing angle β. A mass transfer correlation is also proposed for the square-cell commercial spacer commonly used in RO/NF modules.