On the nature of transonic buffet in a finite span wing

Abstract

Transonic buffet, or self-sustained shock oscillations caused by shock boundary layer interactions, creates lift and drag fluctuation on the wing of an aircraft. This aerodynamic instability limits the flight envelope of an aircraft. In the literature on transonic buffet, in general, there are three approaches to study transonic shock buffet in 2D or 3D flow configurations, namely, cross-correlation-based wave propagation analysis, modal analysis, and global stability theory. In this study, transonic buffet due to shock and turbulent boundary layer interactions, is investigated on the Benchmark SuperCritical Wing (BSCW) from a perspective of critical point theory together with cross-correlation analysis. Critical point theory is used to discern fixed points—stable and unstable foci, saddles, and nodes—present in the skin-friction field obtained from the URANS solution and their influence on the shock buffet. Cross-correlation of the pressure fluctuation on the wing suction and pressure surface is used to determine the pressure wave propagation speed and direction, streamwise and spanwise, caused by convection, or oscillation, of these critical points. This approach is applied to the flow solution obtained from URANS simulations for the three flow conditions for this finite span wing. The first is transonic buffet on the stationary BSCW at Mach 0.85 and a Reynolds number 4.49 x10^6 at different angles of attack, namely, −1, 0, 1, 3, 5, and 7 deg. At this Mach number, the strong shock causes significant shock oscillations on both surfaces of the wing. The second flow condition, on the same wing, is at a Mach number of 0.80 and a Reynolds number of 4 × 10^6, at 5 deg angle of attack. The shock is relatively mild. The third case investigated is the influence of small amplitude— 1deg—pitch oscillations at a frequency close to the transonic buffet frequency, for the Mach 0.8, Reynolds number 4 × 10^6, and 5 deg mean angle of attack test case. In the first problem, a physical mechanism is proposed for self-sustained inboard propagation of buffet cells on the suction and pressure surfaces based on pairs of contra-rotating unstable foci in the separated region. In the second test case at Mach 0.8, a different physical mechanism is proposed for the self-sustained oscillation of buffet cell(s) on the suction surface. In both problems, the frequencies of these buffet cells are in the order of 2D buffet frequencies. In the third problem, forced pitching at a frequency close to the buffet frequency, at a small pitching amplitude, eliminates the propagation of buffet cells and confines the separated region to the root region on the suction surface of the wing.