Using a proper orthogonal decomposition to elucidate features in granular flows

Abstract

Abstract We apply proper orthogonal decomposition (POD) technique to analyze granular rheology in a laboratory-scale pulsed-fluidized bed. POD allows us to describe the inherent dynamics and energy budget in the dominant spatio-temporal modes in addition to identifying spatial coherence. This enables us to elucidate non-linear interactions between the different mechanisms which has been a shortcoming of conventional statistics-based approaches. The bubbling pattern is a result of interplay between the harmonic and sub-harmonic components. The mesoscopic flow features which contribute to the pattern are dependent on the modal energy budget which change with the pulsing frequency. It is also observed that the granular dynamics can be sufficiently reconstructed by the leading POD modes despite the presence of bubbles which represent kinematic shocks contributing to higher-order modes. In short, we highlight the utility of POD while analyzing fluidized granular flows, and pave the way for future analyses. Graphic abstract