System Identification of Two-Dimensional Transonic Buffet

When modeled within the unsteady Reynolds-averaged Navier-Stokes framework, the shock wave dynamics on a two-dimensional airfoil at transonic buffet conditions is characterized by time-periodic oscillations. Given the time series of the lift coefficient at different angles of attack for the OAT15A supercritical profile, the Sparse Identification of Nonlinear Dynamics (SINDy) technique is used to extract a parameterized, interpretable, and minimal-order description of this dynamics. For all the operating conditions considered, SINDy infers that the dynamics in the lift-coefficient time series can be modeled by a simple parameterized Stuart-Landau oscillator, reducing the computation time from hundreds of core hours to seconds. The identified models are then supplemented with equally parameterized low-dimensional dynamic mode decomposition based state observers enabling real-time estimation of the whole flowfield from the predicted lift. The value of this simple model is in the possibility of enriching sparse data sets in the buffet regime for new geometries. Only a few unsteady simulations need to be performed to adjust the coefficients of the identified model and then supplement the data set with new cases. Simplicity, accuracy, and interpretability make the identified model an attractive tool toward the construction of real-time systems to be used during the design, certification, and operational phases of the aircraft life cycle.