Stability boundary prediction of nonlinear transonic buffet via a time-varying modelling method

Transonic shock buffet is a typical flow instability induced by shock-wave/boundary-layer interaction. It exhibits sustained shock oscillations and lift fluctuations, thereby restricting the flight envelope of aircraft. Previous numerical studies have revealed that evident hysteresis envelopes exist between the onset and extinction boundaries of transonic buffet during angle-of-attack sweeps. Hence accurate characterisation of buffet boundaries under representative dynamic manoeuvres is critical for assessing flight safety and expanding the flight envelope. In this study, a time-varying autoregressive with exogenous input model is established by integrating reduced-order and time-varying modelling to predict the buffet boundary under nonlinear transonic dynamic conditions. Specifically, the nonlinear flow evolution during ascending and descending angle-of-attack sweeps is modelled via piecewise linearisation, and the evolutionary trajectory of system stability is derived from state-space representation to characterise when buffet occurs. The influences of pitching rate and sweep direction on the hysteresis characteristics of the buffet onset boundary are investigated. For rate-dependent hysteresis, a lower pitching rate advances the buffet onset boundary under ascending angle-of-attack sweep, and the boundary gradually converges as the pitching rate further decreases. For path-dependent hysteresis, the ascending sweep yields a higher buffet onset angle of attack than the descending sweep, and such discrepancy diminishes gradually with the reduction of pitching rate. In summary, lowering the pitching rate can effectively suppress both types of dynamic hysteresis characteristics. The proposed method offers engineering guidance for monitoring and early warning of time-varying stability in aerospace and mechanical vibration applications.