Dynamic Mode Decomposition of Random Pressure Fields over Bluff Bodies

Abstract

Aerodynamic pressure field over bluff bodies immersed in boundary layer flows is correlated both in space and time. Conventional approaches for the analysis of distributed aerodynamic pressures, e.g., the proper orthogonal decomposition (POD), can only offer relevant spatial patterns in a set of coherent structures. This study provides an operator-theoretic approach that describes dynamic pressure fields in a functional space rather than conventional phase space via the Koopman operator. Subsequently, spectral analysis of the Koopman operator provides a spatiotemporal characterization of the pressure field. An augmented dynamic mode decomposition (DMD) method is proposed to perform the spectral decomposition. The augmentation is achieved by the use of the Takens's embedding theorem, where time delay coordinates are considered. Consequently, the identified eigen-tuples (eigenvalues, eigenvectors, and time evolution) can capture not only dominant spatial structures but also identify each structure with a specific frequency and a corresponding temporal growth/decay. This study encompasses learning the evolution dynamics of the random aerodynamic pressure field over a scaled model of a finite height prism using limited wind tunnel data. The POD analysis of the experimental data was also carried out. To demonstrate the unique feature of the proposed approach, the DMD and POD based learning results including algorithm convergence, data sufficiency, and modal analysis are examined. The ensuing observations offer a glimpse of the complex dynamics of the surface pressure field over bluff bodies that lends insights to features previously masked by conventional analysis approaches.