Behavior of wake flows past porous bluff bodies

In the present thesis, the wake flows at low Reynolds numbers past porous bluff bodies are investigated, in the context of flow control. The mathematical model for the flow inside the porous medium is based on the Volume Averaged Navier Stokes Equations. The resulting formulation takes into account the penetration of the viscous and inertial terms in the porous medium. At the interface between the surface and the pure fluid the continuity of the velocities and stresses is considered. The mathematical model for the flow through a porous medium has been then validated against Direct Numerical Simulations described in the literature, finding an excellent agreement; the presence of the inertial term in the equations is fundamental to well capture the flow behavior near the interface. The stability analysis is carried out within the framework of the global linear stability theory, of the sensitivity analysis and of the local spatio-temporal analysis. The introduced analytic tools have been applied to the case of the porous rectangular cylinders, varying the thickness-to-height ratio, up to the two limit cases of the flat plate and the square cylinder. In all the configurations it is noted that the recirculation bubble detaches from the body and moves downstream, as the permeability is increased. At the same time the recirculation bubble becomes smaller and disappears, resulting in a stabilization of the flow and in an inhibition of the vortex shedding. This behavior has been observed for all values of the Reynolds number. The detachment of the recirculation bubble implies the displacement of the global instability core, that has been verified both with the sensitivity analysis and some Direct Numerical Simulations. Moreover, it is found that, for proper combinations of the flow parameters, the flow is globally unstable but without a recirculation region in the wake. The local spatio-temporal analysis is shown to provide an explanation of this behavior, also demonstrating that the marginal stability curve in the space of the parameters can be related to a specific region in the wake, in which the velocity on the symmetry axis is less than the 5% of the free-stream velocity. The results for different values of the thickness of the rectangular bodies indicate that the behavior is the same introducing a parameter corrected with the thickness-to-height ratio of the rectangular cylinder. The steady and axisymmetric flow, for a disk and a sphere, has also been carried out using the global stability and sensitivity analysis. The results show an analogous behavior to that of the rectangular cylinders, while the flow around a sphere can exhibit a penetrating recirculation bubble, besides the already illustrated phenomena