On the energy of high-frequency characteristics and the lock-in phenomena of transonic buffet

Abstract

Abstract The limit cycle oscillation (LCO) in the transonic buffet on the fixed supercritical airfoil OAT15A under Ma = 0.73, AoA=3.5° and Re≈3×106 , is successfully simulated by means of the Reynolds Stress Model. Higher-frequency characteristics related to vortex shedding is investigated through the sparsity-promoting dynamic mode decomposition (SP-DMD) and the wavenumber-frequency spectrum analysis. The modal analysis on the LCO pressure field reveals that the vortex modes whose frequencies gather around 3000 Hz correspond to acoustic waves and vortex shedding, and these vortex modes contribute quite a bit to the LCO behaviour and interact with the shock according to the energy criterion. On the other hand, the velocities of the shock-induced perturbation, Kelvin-Helmholtz vortices and acoustic waves are clearly identified in the wavenumber-frequency spectrum. Further, the buffet lock-in phenomena under prescribed pitch conditions are also studied by evaluating the energy exchange between the flow and the airfoil. From the energetic point of view, the trough of the energy map indicates the buffet lock-in onset while the upper zero energy exchange boundary offers the exit of the lock-in. The energy exchange between the flow and the airfoil alters the intensity of the shock and triggers the lock-in. Under the coupled interaction between the buffet and the airfoil motion, the onset of the lock-in is lowered compared to the flutter boundary, narrowing the flight envelope.