Data-Driven Unsteady Aerodynamic Modeling for Studying Fluid-Structure Interaction

A class of simplified aerodynamic models, known as piston theory, that link body deformation to localized pressure fluctuation with respect to a mean steady state are attractive for modeling purposes as they constitute a computationally efficient model to calculate the unsteady pressure response on deforming bodies. However, piston theories are only valid for flow regimes where M∞ > 1.5, making these theories incompatible for modeling the aerodynamic response associated with aeroelastic phenomena in the subsonic or low-supersonic flow regimes. To extend the validity of piston theory into these regimes, a framework based on the dynamic mode decomposition (DMD) is presented. Unsteady computational fluid dynamics (CFD) simulations are used to learn the unsteady pressure response and DMD is applied to the error between the CFD computed pressure fluctuation and the piston theory predicted pressure fluctuation. This process is performed on two-dimensional and three-dimensional flow domains over a variety of flow regimes. For both scenarios, the DMD analysis learns dominant spatial modes in the error that constitute low-order models which may be used to improve the pressure response and are confirmed to be physically relevant. A method for computing aeroelastic stability with these leading modes is discussed and applied to fluid-structural beam and panel configurations. The results are compared against prior numerical and experimental investigations to quantify the improvement in prediction obtained by the DMD-augmented piston theory.