Proper orthogonal decomposition, dynamic mode decomposition, wavelet and cross wavelet analysis of a sloshing flow

Internal hydrodynamics and its coupling with structural dynamics are non-negligible processes in the design phase of aerospace systems. An improved understanding of the nature of this coupling would allow for greater flexibility in modeling and design of such systems, and could lead eventually to the development of suitable active and/or passive control strategies for enhanced performances. In this manuscript we apply a number of data analysis techniques: proper orthogonal decomposition, dynamic mode decomposition and wavelet transform and their combination to time-resolved images of a liquid sloshing within an enclosure. We use these techniques to identify fluid-dynamic modes in space and time and to verify their coupling with the structural dynamics of vibrating structures. In particular we consider the transient case of a water tank mounted on a free oscillating cantilever. As the acceleration amplitude decays, we observe and quantify the transition from incoherent flow to standing waves. Our results show that the content of the images is very informative and can be used for quantitative analysis. As the main outcome, the hydrodynamic modes are identified using POD and DMD, and related to known features of sloshing flow, such as the frequency of the first symmetric free surface mode. Additionally we perform a comparison of wavelet transforms of POD time coefficients and measured acceleration signals at the tank base. Viewing the latter as the input and the former as the output of the fluid-dynamic system, we are able to correlate the enhanced damping of the cantilever oscillation to the different regimes of the hydrodynamic field.