Direct Numerical Simulations of a Separating Turbulent Boundary Layer Subjected to Zero-Net-Mass-Flux Actuation*

The response of a turbulent separation bubble (TSB) to zero-net-mass-flux actuations is investigated via DNS. The TSB is formed by applying a suction-only velocity profile on the top boundary. Streamwise-oriented actuators are placed upstream of the TSB to produce perturbations mimicking the G\"{o}rtler vortices that cause a low-frequency unsteadiness of the TSB. The natural vortex-shedding frequency ($f_h$) and breathing/flapping frequency ($f_l=0.4f_h$) of the undisturbed TSB are examined, as well as another one at 10$f_l$. Compared with the undisturbed case, the TSBs under the actuation at $f_h$ and $f_l$ reattach earlier, leading to a 50\% reduction in length and improved pressure recovery. The low-frequency unsteadiness is amplified, showing as a periodic formation of clockwise-rotating large vortices at $f_l$. Actuation at $10f_l$ barely changes the TSB and even causes more pressure loss. The response preference of the TSB to certain actuation frequencies is further discussed by a spectral analysis of a harmonic resolvent operator performed to a base flow that consists of the mean and the low-frequency unsteady motion. The preferred perturbation and the receptivity of the mean flow to actuation at different frequencies suggested by analysis are consistent with the DNS.