System Identification of Two-Dimensional Transonic Buffet

Abstract

When modeled within the unsteady Reynolds-Averaged Navier-Stokes framework, the shock-wave dynamics on a two-dimensional aerofoil 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 parametrized, interpretable and minimal-order description of this dynamics. For all of the operating conditions considered, SINDy infers that the dynamics in the lift coefficient time series can be modeled by a simple parametrized Stuart-Landau oscillator, reducing the computation time from hundreds of core hours to seconds. The identified models are then supplemented with equally parametrized measurement equations and low-rank DMD representation of the instantaneous state vector to reconstruct the true lift signal and enable real-time estimation of the whole flow field. Simplicity, accuracy and interpretability make the identified model a very attractive tool towards the construction of real-time systems to be used during the design, certification and operational phases of the aircraft life cycle.