This study presents a numerical prediction of the flutter boundary for the NACA0012 benchmark wing, with particular emphasis on the effects of the wing-root wall and secondary flows. The unsteady Reynolds-averaged Navier–Stokes equations are solved using the Spalart–Allmaras (SA) turbulence model with a Quadratic Constitutive Relation (SA-QCR, 2024 version), while the wing motion is modeled as a two-degree-of-freedom system. Both the wing-root wall condition and the QCR significantly impact the prediction of the strong instability regime at high Mach numbers in the NACA0012 benchmark wing. Flowfield analysis further shows that this combined modeling captures secondary flows in the wing-root corner, suppresses corner separation, and thereby exerts a critical influence on predicting the strong instability regime at high Mach numbers. In addition, energy-transfer analysis reveals that a negative lift slope, which promotes positive energy transfer from the fluid to the structure, serves as the primary mechanism driving the observed strong instability. This negative lift slope arises from the upstream movement of the shock wave over the upper surface as the angle of attack increases.
Miyake et al. (Mon,) studied this question.