Modal Analysis of Sparse Surface Pressure Measurements in Highly Unsteady Aerodynamic Flows

Focusing on an airfoil with pitching and plunging motions as well as a more complex delta wing experiencing gusts, we leverage linear proper orthogonal decomposition (POD) and two nonlinear autoencoders (AEs) to elucidate patterns in sparse surface pressure for highly unsteady aerodynamic problems. For the airfoil, both POD and AEs effectively decomposed and reconstructed the surface pressure data with only three modes or latent variables. Additionally, the first three POD modes distinctively identified key features of the surface pressure associated with the pitching and plunging motions. For the more complex delta wing case, both POD and AEs achieved accurate reconstruction using only three latent variables. However, the linear POD worked particularly well not only in surface pressure reconstruction but also in revealing physical insights: the identified modes were found to be intrinsically related to the mean flow structure, the Reynolds number, and the angle of attack, which were verified by the clusters in the identified low-dimensional manifold. These findings reveal that despite nonlinear flow complexities, underlying low-dimensional structures exist in surface pressure measurements, offering a new paradigm for aerodynamic state monitoring and manipulation.