Computational fluid dynamics simulations of unsteady mixing in spacer-filled direct contact membrane distillation channels

Direct contact membrane distillation (DCMD) is a promising means of concentrating brines to their saturation limit. During that process, membrane spacers play a key role in temperature polarization, concentration polarization, and mineral scaling. These interactions are not well understood, because they are difficult to study experimentally and numerically, and the flow regimes are not fully charted. We consequently develop a tailored in-house CFD code that simulates unsteady two-dimensional heat and mass transport in plate-and-frame DCMD systems with cylindrical spacers. The code uses a combination of finite-volume methods in space, projection methods in time, and recent advances in immersed boundary methods for the spacer surfaces. Using the code, we explore how the transition to unsteady laminar vortex shedding affects polarization and permeate production of DCMD systems. We show that the impact of spacers can be explained by examining the various steady and unsteady vortical flow structures generated in the bulk and near the membranes. Overall, we show that though unsteady vortex structures tend to mix temperature polarization layers with the bulk, they are not similarly able to mix the concentration layers. Rather, vortical structures tend to create regions of preferential salt accumulation. In the vortex shedding regime, the net result is that spacers often increase vapor production at the expense of increasing the risk of mineral scaling.