Data-driven modeling of transonic unsteady flows and efficient analysis of fluid–structure stability

The reduced-order aerodynamic models constructed via the linear/nonlinear system identification methodologies cannot reveal the flow characteristics of the fluid–structure coupling system because the state variables of the reduced-order model do not explicitly represent fluidic properties. In this study, a data-driven modeling procedure is proposed to reconstruct a physics-based, reduced-order aerodynamic model. In the procedure, the transonic unsteady flows of concern are projected onto low-dimensional base vectors first via the proper orthogonal decomposition of pressure snapshots subject to a specific structural excitation. Then a state-space representation of the temporal coefficients of proper orthogonal decomposition modes subject to the structural excitation is established by using the dynamic mode decomposition with control. Finally, for the fluid–structure stability analysis, pressure snapshots are recovered from the coefficients of proper orthogonal decomposition, and aerodynamic forces are derived by integrating the pressure coefficients around the wing surface. The state vector in above-mentioned data-driven model has a clear sense in physics with regard to pressure distribution. To demonstrate the accuracy of the proposed procedure, a two-dimensional, transonic aeroelastic wing with an NACA0012 profile is studied. The unsteady aerodynamic forces, frequency responses of the reduced-order aerodynamic model, transonic flutter boundary, and flow characteristics at the flutter condition are predicted and compared with direct computational fluid dynamic simulations. The results show that the modeling procedure can accurately predict the transonic flutter boundary and flow characteristics.