Annular Flow Between Rotating Porous Discs with Pressure-Driven Wall-Normal Permeation

Rotating disc systems generate distinctive flow patterns characterized by boundary-layer acceleration due to Coriolis forces and the formation of Ekman layers near no-slip surfaces. When these surfaces are porous, the resulting pressure buildup induces wall-normal permeation, which dynamically alters the overall flow behavior. This configuration introduces a strong two-way coupling between pressure and flux, modifying both the canonical Ekman layer structure and global flow behavior. In this study, we implement a pressure-coupled permeation model, where the flux through rotating porous walls evolves in response to local hydrodynamic pressure. Using high-fidelity CFD simulations, we examine how this coupling reshapes flow structure and pressure distribution in the annular domain between co-rotating discs. While Ekman layers remain a dominant feature, the addition of pressure-driven permeation modifies their structure, wall shear, and the radial pressure gradient. We find that the transition from a Poiseuille-like core profile to Ekman-dominated flow is influenced by the induced axial flux, leading to an advective shift in flow regime. Importantly, the implementation of pressure-coupled flux requires careful numerical treatment, as it introduces a strong coupling between momentum and mass continuity at the permeable boundaries. These findings offer new insights into control and design of rotating membrane systems and separation technologies.