Characterizing flow and pressure dynamics of annulus flow between two rotating permeable discs*

This study investigates the hydrodynamics of incompressible annular flow between two uniformly rotating, porous discs, in contrast to previous research focused on impermeable discs. The porous nature of these discs introduces no-slip but selectively permeable boundary conditions, significantly modifying the velocity and shear profiles. Through highly resolved laminar and LES simulations, we examine the effects of mass transfer through the porous medium on bulk flow dynamics, with flow rates through the discs reaching up to 50% of the inlet flow. Our findings reveal that the formation of Ekman layers, characterized by high peak velocities near the walls, plays a crucial role in determining the wall shear stress distribution and influencing the advective behavior of species near the wall. Additionally, the combined effects of rotation-induced centrifugal force and wall flux reduce the bulk flow rate, profoundly affecting the radial pressure distribution. Understanding these pressure dynamics is essential, as they are key drivers of the pressure-driven separation process by impacting local flux. Overall, this study aims to show how these altered flow dynamics theoretically influence the conditions that affect species transport, leading to accumulation along the porous surfaces. By characterizing pressure dynamics and shear profiles under varying rotation rates, flow rates, and flux rates, we aim to optimize separation efficiency in pressure-driven systems.