Flow physics of progressive-curvature Coanda surfaces in transonic circulation control

Abstract

Premature jet separation severely limits the control authority of transonic circulation control (CC) airfoils. This study investigates the flow physics governing Coanda jet attachment and develops a progressive-curvature Coanda surface at Ma=0.72 through shape optimization of the NASA-SC(2)-0714-CC supercritical airfoil. Relative to the constant-radius baseline, the optimized progressive-curvature surface achieves 37.0% lift enhancement and extends jet deflection from 79.4° to 125.0°. Flow-field analysis shows that the performance improvement is governed by two coordinated curvature effects. A locally smaller curvature radius near the slot exit lets the under-expanded jet expand more fully along the wall. A confined shock-induced separation bubble is then bridged and reattached, and shock-cell oscillations are damped. The subsequent progressive increase in the curvature radius reduces the required centripetal acceleration as the jet momentum decays, thereby sustaining the wall-normal pressure gradient and delaying separation. The optimized geometry also retains its effectiveness at Ma=0.3, yielding 23.2% higher lift-to-drag ratio than the baseline configuration. These results demonstrate that matching surface curvature to evolving jet momentum governs transonic CC effectiveness.