Global stability analysis of 2D and fully 3D incompressible flows with applications to flow control

Numerical tools for global linear stability and sensitivity analyses in fluid dynamics are developed in the present work. These tools are applied to the investigation and control of two- and three-dimensional internal flow configurations. The first application is to the flow in a two-dimensional symmetric channel with a sudden expansion. The laminar flow in such diffusers may produce either symmetric or nonsymmetric steady solutions, depending on the value of the Reynolds number as compared with some critical value. The stability properties of the flow are studied in the context of linear theory. In this context, a sensitivity analysis of the flow instability is carried out with respect to perturbations that may be produced by a realistic passive control, thus providing qualitative hints and quantitative information for the control design. Following the so-obtained information, a passive control is built by introducing a small cylinder in the flow with the aim of stabilizing the unstable symmetric flow configuration in the diffuser. The effectiveness of this control is finally assessed by direct numerical simulation. It is shown that the introduction of the cylinder, placed following the indications of the linear sensitivity analysis in the stable asymmetric flow configuration, allows a steady completely symmetric or less asymmetric flow to be recovered. The flow transient between the uncontrolled asymmetric solution and the symmetric controlled one is analyzed in terms of streamlines and vorticity evolution; the effects of the cylinder introduction on flow dissipation are also assessed. A further application to the study of the fully three-dimensional instabilities occurring in the flow in micro T-mixers is presented. First, the instability leading to the steady engulfment regime is characterized by the computation of the critical Reynolds number and of the global unstable mode for different T-mixer geometries with fully-developed inlet velocity conditions. Direct numerical simulations (DNS) are also carried ...