Global stability, sensitivity and passive control of low-Reynolds-number flows around NACA 4412 swept wings. (25th February 2023)

• Record Type: Journal Article
• Authors: Nastro, G.; Robinet, J.-C.; Loiseau, J.-C.; Passaggia, P.-Y.; Mazellier, N.
• Is Part Of: Journal of fluid mechanics. Volume 957(2023)
• Publication Date: 2023-02-25
• Subjects: boundary layer separation -- instability control -- wakes; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2023.41
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : 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 ${\textit {Re}}$ and angles of attack $\alpha$ . The wake dynamics is driven by the two-dimensional von Kármán mode whose emergence threshold in the $\alpha \unicode{x2013}{\textit {Re}}$ 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 Kármán 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 Kármán 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 Kármán 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.