Transonic buffet instability: From two-dimensional airfoils to three-dimensional swept wings

The objective of the present study is to explain the evolution of the transonic buffet phenomenon from two-dimensional airfoils to three-dimensional swept wings by a global stability analysis. With respect to two-dimensional buffet, shock oscillation frequency increases by a factor of 4 to 7 in the case of a swept 30◦ wing and three-dimensional patterns in the detached boundary layer are convected outboard. Crouch et al. [J. Comput. Phys. 224, 924 (2007)] explained the two-dimensional transonic buffet phenomenon by the appearance of a real positive complex eigenvalue of the linearized Jacobian matrix. In the case of an infinite unswept wing, the present study shows that two unstable modes actually exist: The two-dimensional transonic buffet mode already identified by Crouch et al. [J. Fluid Mech. 628, 357 (2009)] and a strongly amplified three-dimensional zerofrequency mode. The latter exhibits regular patterns in the separated boundary layer, which relates to the so-called buffet cells as named by Iovnovich et al. [AIAA J. 53, 449 (2015)]. The nonzero sweep angle generates a spanwise velocity component on the wing which convects the cells outboard. This impacts both modes identified in the unswept case: The two-dimensional mode is weakly damped by the sweep while the three-dimensional buffet cells mode, even if weakly damped, remains strongly unstable and now exhibits a nonzero frequency which increases with the sweep angle. The frequency and wavelength of the most unstable three-dimensional mode for a sweep angle of 30◦ agree well with numerical and experimental values of the three-dimensional transonic buffet on wings. The analysis of the wavemaker of the three-dimensional modes indicates that the core of the instability is nearly solely located in the separated region, with a maximum along the separation line. In contrast, the wavemaker of the two-dimensional buffet mode exhibits stronger values all along the shock wave