Numerical study of the hysteresis effect on the supercritical airfoil for the transonic circulation control

Circulation Control (CC) has been attracting increasing attention because of its potential to replace traditional control surfaces. One of the bottlenecks that restrict the further application of the CC technology to the transonic flight control is the separation of the supersonic CC jet, which is usually accompanied by hysteresis. In this study, the hysteresis effect of the CC technology on the ONERA OAT15A supercritical airfoil is numerically studied with the transonic freestream conditions Ma=0.73, α=2.5°, and Re_c≈3.0×10⁶. Results indicate that there is a significant hysteresis between the jet separation and the reattachment. Furthermore, the mechanisms of the CC jet separation and reattachment are obtained by analyzing the development of the jet flow. Finally, four different CC devices are investigated to show that the hysteresis effect of the CC technology can be effectively reduced by increasing the radius-to-slot ratio, setting a step between the slot exit and the Coanda surface, and employing a convergent-divergent nozzle.