Stability analysis and control of the flow in a symmetric channel with a sudden expansion

The laminar flow in two-dimensional 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. © 2012 American Institute of Physics.