Optimal Position and Angle of Jet Control for Transonic Shock Buffet with Resolvent Analysis

Transonic shock buffet refers to the phenomenon of significant oscillation of shock waves during transonic flight. Due to its strong unsteady and nonlinear characteristics, effective control of buffet has consistently posed a challenge. In this study, a physics-guided active control framework is proposed to stabilize the unsteadiness of buffet, in which the core control parameters are determined by the resolvent analysis and dominant flow features. Based on the unstable steady base flow, resolvent analysis is first conducted on buffet flow over the NACA0012 airfoil. The obtained forcing mode exhibits an obvious oblique characteristic on the upper surface of the airfoil, representing that the buffet flow is most sensitive to external forcing in this region, like an acupoint. Following this guidance, a steady jet active control with a very tiny momentum coefficient is then applied at this position. The results of different jet positions and angles from numerical simulation indicate that the jet can suppress shock buffet only within the narrow region guided by the forcing mode. The correlation between flow features obtained from resolvent analysis and optimal control patterns is quantitatively established by effective gains, which explain that the selection of jet control position and angle is essentially a flow sensitivity problem.