Modeling of flow and mass transfer dynamics in spacer-filled channels of membrane processes using direct numerical simulations

Abstract

This study evaluates the effect of different flow regimes on the local and global mass transfer coefficient for feed spacer-filled channels in membrane separation processes using Direct Numerical Simulation (DNS). The computational domain was built with arrangements of multiple spacer units based on accurate three-dimensional CT scan of a commercial reverse osmosis feed-spacer. Hydrodynamics was coupled with solute transport and a permeable membrane. Computations were performed in two membrane/spacer configurations: (i) spacer “floating” within the feed channel and (ii) spacer “touching” the membrane, both in a wide range of inlet channel velocities (2 – 60 cm/s). The observed flow-regime was categorized based on dynamics (steady vs. periodic vs. unsteady), subdividing the laminar steady regime based on spatial distribution (regular vs irregular), resulting in four observed regimes: regular laminar-steady, irregular laminar-steady, periodic and unstable, depending on velocity and position. Transition from laminar-steady to unsteady flow occurred for Re > 950 (“floating”) and 720 (“touching”). When more than four spacer cells are considered, different flow-regimes can occur simultaneously at different locations in the channel. Instabilities within the flow arising from external perturbation can trigger unstable flow only at high velocities (40 cm/s), indicating that at industrial conditions (velocity < 16 cm/s) it would be difficult to perturb the flow in a meaningful way. Vortex analysis showed how the spacer works as a static mixer, promoting the splitting and rotation of flow. Furthermore, in the unsteady flow, the presence of vortices traveling within the feed channel assists the transport of solute from the membrane to the bulk, renewing the polarization layer. Finally, the effect of each flow regime on the mass transfer coefficient was shown in the traditional Sh-Re power law ($Sh=aR{e}^{b}S{c}^c$), where the exponent b varied from the expected 1/3 in the laminar-steady flow to ca. 0.9 in the transitional regime.