Using a proper orthogonal decomposition to elucidate features in granular flows

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

Proper orthogonal decomposition of ice velocity identifies drivers of flow variability at Sermeq Kujalleq (Jakobshavn Isbræ)

“…More recently, however, the ability of a POD to extract spatial pictures of regions of coherence has resulted in successes in relatable fields, e.g. fluvial hydrodynamics (Higham et al, 2017), granular rheology (Higham et al, 2020), and solar flare magnetohydrodynamics (Albidah et al, 2020).…”

A new approach to proper orthogonal decomposition with difference quotients

“…Because of the efficiency of POD ROMs, they are used in many applications including control theory and fluid dynamics to solve computationally demanding problems. For a small selection of applications see, e.g., [1,3,10,14,20,23,24,27,32,38,42,43,47].…”

Anomalous Diffusion in a Bench-Scale Pulsed Fluidized Bed

“…Individual tracks were determined by Optical Flow Equations, and the outliers were detected based on proper orthogonal decomposition technique [32]. Further details regarding the experiments have been avoided for the sake of brevity, and can be found in Higham et al [12].…”

“…PFBs have shown improved hydrodynamics by reducing or eliminating channeling or clumping of particles, and enhanced heat and mass transfer properties while being non-intrusive. Studies in the past have primarily reported on the meso-scale and macro-scale observations in PFBs [7][8][9][10][11][12]. Persistent interactions between dynamical modes are present at different scales, and particle-level description is pivotal in elucidating some of the observed features.…”

“…GDP is sub-diffusive (γ < 1) when α > 2β + 4, and super-diffusive (γ > 1) otherwise. Based on the physics of PFB as explained in our previous study [12], we hypothesize the system hosts a combination of parent processes discussed above, as will be shown in the remainder of this article. We also study the effect of ageing i.e., the time lapsed after initializing an experiment.…”