Numerical Analysis and Prediction of Transonic Lateral Instability in the SDM Configuration

This study investigates the physical mechanism underlying the transonic wing rock phenomenon observed in highly maneuverable aircraft using a combination of unsteady Reynolds-averaged Navier-Stokes (URANS) simulations, dynamic mode decomposition (DMD), energy-based analysis, and global stability analysis (GSA). The unsteady rolling motion of the standard dynamics model (SDM) is simulated by coupling the URANS equations with a rotational dynamics equation. The numerical approach is validated against wind tunnel data, showing good agreement in both steady aerodynamic characteristics and unsteady rolling behavior, including onset prediction and surface pressure distributions measured by pressure-sensitive paint (PSP). DMD analysis reveals dominant coherent structures associated with the wing rock, highlighting shock oscillation near the main wing tip as a key contributor to the instability. An energy-based approach further confirms that this shock motion plays a central role in sustaining the oscillation by transferring kinetic energy from the flow to the model dynamics. The same mechanism is shown to drive the bifurcation between stable and unstable states at the onset of wing rock. To predict the onset of the instability which induced by the shock oscillation, we try to apply GSA as it has been used to predict shock instability phenomenon such as the transonic buffet. The results identify unstable global modes in the same pitch angle range where wing rock is observed experimentally and numerically, and the extracted modes correspond to shock-related fluctuations. Compared to time-domain URANS computations, the GSA approach provides a significant reduction in computational cost, suggesting its potential as a practical tool for early prediction of lateral instabilities in aircraft design.