Application of projection and immersed boundary methods to simulating heat and mass transport in membrane distillation

Abstract

Membrane distillation is an emerging desalination process with important applications to the energy-water nexus. Its performance depends, however, on heat and mass transport phenomena that are uniquely challenging to simulate. Difficulties include two adjacent channel flows coupled by heat and mass transport across a semi-permeable membrane. Within the channels, heat and mass boundary layers interact with the membrane surface and vortical flow structures generated by complicated geometries. The presence of multiple inlets and outlets also complicates the application of mass-conserving outlet conditions. Moreover, even small amounts of outlet noise affect the resolution of important near-membrane fluid velocities. We show these phenomena can be simulated to second-order spatial and temporal accuracy using finite volume methods with immersed boundaries and projection methods. Our approach includes a projection method that staggers the coupled channel flows and applies Robin boundary conditions to facilitate mass conservation at the outlets. We also develop an immersed boundary method that applies Neumann boundary conditions to second-order spatial accuracy. The methods are verified and validated against manufactured solutions and theoretical predictions of vortex shedding. They are then applied to the simulation of steady and unsteady transport phenomena in membrane distillation. The methods have important applications to the broad field of chemical engineering and deal with long-standing issues in both theoretical and computational fluid dynamics.