Effects of a zero normal-concentration-gradient outflow boundary condition on concentration polarization in a CFD study of a reverse osmosis process

Abstract

Numerically modeling only part of the reverse osmosis channel and assuming that the concentration gradient is zero at the outflow is common practice. In the present work, the effect of this hypothesis on concentration polarization and its validity are numerically investigated. The reverse osmosis system considered consists of two parallel walls. The top wall is assumed to be impermeable and a membrane is placed at the bottom wall. To investigate the hypothesis of zero concentration gradient at the outflow, two different cases are considered. In the first case, the membrane occupies the full-bottom wall, while in the second case, the membrane is followed by an impermeable wall section to ensure a steady-state concentration at the channel outlet. The finite volume method is used to solve the governing equations. In order to check the accuracy of our computational code, the simulated results for the first case without an impermeable section are validated against numerical simulations available in the literature. The simulation results show that the choice of the boundary condition at the outlet channel considered by most authors is not always obvious. This assumption leads to an under-evaluation of the membrane concentration. The deviation reaches 20% for short membrane lengths and low feed concentrations.