Global stability, sensitivity and passive control of low-Reynolds-number flows around NACA 4412 swept wings

The stability and sensitivity of two-and three-dimensional global modes developing on steady spanwise-homogeneous laminar separated flows around NACA 4412 swept wings are numerically investigated for different Reynolds numbers Re and angles of attack alpha. The wake dynamics is driven by the two-dimensional von Karman mode whose emergence threshold in the alpha-Re plane is computed with that of the three-dimensional centrifugal mode. At the critical Reynolds number, the Strouhal number, the streamwise wavenumber of the von Karman mode and the spanwise wavenumber of the leading three-dimensional centrifugal mode scale as a power law of alpha. The introduction of a sweep angle attenuates the growth of all unstable modes and entails a Doppler effect in the leading modes' dynamics and a shift towards non-zero frequencies of the three-dimensional centrifugal modes. These are found to be non-dispersive as opposed to the von Karman modes. The sensitivity of the leading global modes is investigated in the vicinity of the critical conditions through adjoint-based methods. The growth-rate sensitivity map displays a region on the suction side of the wing, wherein a streamwise-oriented force has a net stabilising effect, comparable to what could have been obtained inside the recirculation bubble. In agreement with the predictions of the sensitivity analysis, a spanwise-homogeneous force suppresses the Hopf bifurcation and stabilises the entire branch of von Karman modes. In the limit of small amplitudes, passive control via spanwise-wavy forcing produces a stabilising effect similar to that of a spanwise-homogeneous control and is more effective than localised spherical forces.