Using a proper orthogonal decomposition to elucidate features in granular flows
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ORIGINAL PAPER
Using a proper orthogonal decomposition to elucidate features in granular flows J. E. Higham1 · M. Shahnam2 · A. Vaidheeswaran2 Received: 3 January 2020 © The Author(s) 2020
Abstract We apply proper orthogonal decomposition (POD) technique to analyze granular rheology in a laboratory-scale pulsedfluidized 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. Keywords Proper orthogonal decomposition · Pulsed-fluidized bed · Bubbling bed · Granular
1 Introduction Fluidization involves modifying the characteristics of particle-phase to behave as a fluid, thereby enhancing mixing and heat transfer properties. It is common in several industrial applications including combustion, gasification, catalytic cracking and food processing [29]. Of particular interest is dense-bubbling fluidization, which is the most common mode of operation in large-scale systems. However, it is difficult to control the homogeneity of properties like temperature and species composition. This is largely due to voids or bubbles which provide paths of least resistance to the gas phase leading to minimal contact with the solid particles. Besides, there is cascade of energy in the particlephase through inelastic collisions between neighbouring particles as well as particle and wall. Thus, complex
* J. E. Higham [email protected] 1
School of Environmental Sciences, Department of Geography and Planning, University of Liverpool, Roxby Building, Liverpool L69 7ZT, UK
US Department of Energy, National Energy Technology Laboratory, 3610 Collins Ferry Rd, Morgantown, WV, USA
2
inter-phase and particle interactions result in a highly nonlinear system [14]. Previous studies [10, 13, 27, 36, 40, 46] have shown that bubbling could be controlled using a periodic pulsation of gas flow at the inlet, and subsequently the setup is termed pulsed-fluidized bed. Research on these systems is primarily restricted to analyzing the effect of particle characteristics [18, 30] or inlet gas properties [6, 8, 13, 36] on the flow structures. Recently, pulsed-fluidized beds have been used to demonstrate enhanced fluidization, mixing and heat transfer characteristics [1–3, 25, 31, 32]. Despite its growing popularity, a thoro
