Fluid Dynamics and Mass Transfer in Spacer-Filled Membrane Channels: Effect of Uniform Channel-Gap Reduction Due to Fouling
The time-varying flow field in spacer-filled channels of spiral-wound membrane (SWM) modules is mainly due to the development of fouling layers on the membranes that modify the channel geometry. The present study is part of an approach to tackling this extremely difficult dynamic problem at a small spatial scale, by uncoupling the fluid dynamics and mass transfer from the fouling-layer growth process. Therefore, fluid dynamics and mass transfer are studied for a spacer-filled channel whose geometry is altered by a uniform deposit thickness h. For this purpose, 3D direct numerical simulations are performed employing the “unit cell” approach with periodic boundary conditions. Specific thickness values are considered in the range 2.5–10% of the spacer-filament diameter D as well as other conditions of practical significance. The qualitative characteristics of the altered flow field are found to be very similar to those of the reference geometry with no gap reduction. For a given flow rate, the pressure drop, time-average wall-shear stresses and mass-transfer coefficients significantly increase with increasing thickness h due to reduced channel-gap, as expected. Correlations are obtained, applicable at the “unit cell” scale, of the friction factor f and Sherwood number Sh, which exhibit similar functional dependence of f and Sh on the Reynolds and Schmidt numbers as in the reference no-fouling case. In these correlations the effect of channel-gap reduction is incorporated, permitting predictions in the studied range of fouling-layer thickness (h/D) = 0–0.10. The usefulness of the new results and correlations is discussed in the context of ongoing research toward improved modeling and dynamic simulation of SWM-module operation.