On the wake stability of permeable disks

We numerically investigate the flow around three-dimensional permeable disks at Reynolds numbers (Re) ranging from 30 to 500, and Darcy numbers (Da) ranging from 10^-9 to 10^-2. Numerical simulations are performed to examine the effects of permeability on the wake stability of permeable disks with the open-source CFD package OpenFOAM. The continuity and the Darcy-Brinkman equations are solved for the incompressible flow within the computational domain using a customised porousPimpleFoam solver. First, the boundary for the steady-to-unsteady transition is determined using the Stuart-Landau model. When Da < 10^-6, the critical Re for transition remains identical to that of an impervious disk. However, as Da approaches 10^-4, increasing permeability enhances wake stability and delays the onset of unsteadiness, and no unsteady wake is observed for Da ≥ 2×10^-4, indicating a strong stabilising effect of permeability. The dynamical transition route from steady to periodic to chaotic flow is further characterised for permeable disks. Wake patterns are classified into five regimes: steady symmetric, steady asymmetric, periodic, quasi-periodic, and chaotic states. For Da < 10^-4, all flow regimes persist. The dynamical transition route is the same as that of the impervious disk, with the Re boundaries for bifurcations shifting to higher values as Da increases. At Da = 2×10^-4, all unsteady transitions are suppressed, the flow transitions only from a steady symmetric to a steady asymmetric state and then returns to a symmetric state as Re increases. As Da increases further, even the steady bifurcation behaviour observed at the steady state is no longer present for sufficiently high permeabilities (Da ≥ 2.5×10^-4), and the flow remains in a steady symmetric state across the entire Re range considered. These findings highlight the potential for controlling the wake stability of stationary and free-falling disks by exploitingthrough permeability.