Ground-induced suppression of chaos in the self-excited flow behind a plunging airfoil

Abstract

We numerically investigate the forced synchronization of the self-excited flow behind a plunging airfoil in ground effect at a Reynolds number of Re = 1000. On varying the plunging amplitude and frequency, we find a rich array of nonlinear dynamics, such as a period-1 limit cycle due to natural vortex shedding as well as two-frequency quasiperiodicity on a torus attractor (T2). For certain non-resonant plunging frequencies without a ground surface, we find that low-dimensional chaos emerges via the Ruelle–Takens–Newhouse route. However, we find that the chaos can be suppressed by introducing a ground surface, inducing a direct transition from T2 quasiperiodicity to 1:1 phase locking as the plunging amplitude rises over the boundaries of the Arnold tongue. Apart from suppressing chaos, the ground surface also causes the lift and drag coefficients to become less sensitive to the plunging motion itself. Knowledge of the critical plunging conditions required for forced synchronization and chaos could be useful in various engineering applications, such as the design of pico air vehicles.