Abstract
The hydrodynamics of electrodialysis and reverse electrodialysis is commonly studied by neglecting membrane deformation caused by transmembrane pressure (TMP). However, large frictional pressure drops and differences in fluid velocity or physical properties in adjacent channels may lead to significant TMP values. In previous works, we conducted one-way coupled structural-CFD simulations at the scale of one periodic unit of a profiled membrane/channel assembly and computed its deformation and frictional characteristics as functions of TMP. In this work, a novel fluid–structure interaction model is presented, which predicts, at the channel pair scale, the changes in flow distribution associated with membrane deformations. The continuity and Darcy equations are solved in two adjacent channels by treating them as porous media and using the previous CFD results to express their hydraulic permeability as a function of the local TMP. Results are presented for square stacks of 0.6-m sides in cross and counter flow at superficial velocities of 1 to 10 cm/s. At low velocities, the corresponding low TMP does not significantly affect the flow distribution. As the velocity increases, the larger membrane deformation causes significant fluid redistribution. In the cross flow, the departure of the local superficial velocity from a mean value of 10 cm/s ranges between −27% and +39%.
Highlights
Introductionreverse electrodialysis (RED) and ED units consist of a series of anion- and cation-exchange membranes alternately stacked and kept separated by means of spacers or built-in profiles, which define the channels through which the two solutions flow
The superficial velocity distribution, map (e), is qualitatively similar to that in ED/reverse electrodialysis (RED) stacks in the presence of membrane deformations arising from the pressure difference obtained in the undeformed case (Figure 15d), but its mean value 〈 〉 is ~7.5 cm/s, ~12% lower between channels pressure, transmembrane pressure (TMP)).This
Darcy equations in two neighboring channels, treated as porous media, asymmetric behavior of the hydraulic permeability, which varies less under compression than under taking into account the spatial variation of their hydraulic permeability as a function of the local
Summary
RED and ED units consist of a series of anion- and cation-exchange membranes alternately stacked and kept separated by means of spacers or built-in profiles, which define the channels through which the two solutions flow. The hydrodynamics in the fluid-filled channels has a significant impact on several process aspects, such as the pressure drop and mass transfer. For large-scale stacks, model simulations showed that the partial pressure drop in the branches could become dominant, leading to significant deviations from a uniform fluid flow distribution. Since the swelling degrees of the anion- and cation-exchange membranes used were found to be slightly different, the dimensions of the resulting corrugations were different and in some regions of the fluid compartments, did not align perfectly well, which might cause channel deformations that affect flow patterns and mixing
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