Analysis of Wing Section Circulation Control Jet Bistability at Transonic Speeds

The phenomenon of stable lift oscillations occurring on an elliptic wing section utilizing circulation control at transonic speeds was evaluated using numerical simulations. As the momentum of the jet increases beyond a prescribed magnitude, periodic detachment occurs from the trailing edge. This behavior conforms to a bistable state, consistent with prior experimental observations. Analysis by both steady and unsteady Reynolds-averaged Navier–Stokes calculations showed that the effect is decoupled from the dominant upstream shock wave. This indicates that the jet can no longer augment the wing’s circulation, marking the termination of circulation control. Furthermore, the results confirm that the absence of the downstream separation bubble acts as the catalyst for this detachment. Dynamic mode decomposition analysis revealed that the bistability is driven by a pressure feedback between the trailing-edge shock wave and a downstream pressure bubble. Secondary feedback governs the pressure redistribution during the detachment cycle. It was concluded that the pressure-dominant nature of the bistability allows it to be captured using relatively simple methods and even approximated through a reduced-order model comprising only 2% of the total modes, encapsulating 25% of the modal influence and reconstructing the pressure field with 98% accuracy.