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 char- acterized 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 dy- namics (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 sec- onds. 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.