Proper-orthogonal decomposition of spatio-temporal patterns in fluidized beds
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Numerical simulations of the hydrodynamics of a fluidized bed are carried out to investigate the complex interaction between the gas and the solid particles, and to explore the utility of a reduced-order model based on the proper orthogonal decomposition (POD). The behavior of a fluidized bed is modeled using a "two- fluid" theory, which involves conservation of mass, momentum, energy and species equations for the two interpenetrating continua. These equations are solved using a numerical algorithm that employs a conservative discretization scheme with mixed implicit and explicit formulations. We conducted simulations of gas-solid interaction in a narrow (two-dimensional) bed filled with sand particles which was uniformly fluidized at minimum fluidization but with additional air flow through a central nozzle. Aided by the proper orthogonal decomposition, spatial dominant features are identified and separated from the spatio-temporal dynamics of the simulations. The most dynamic region of the gas-solid interaction is confined to the central channel caused by the jet. The flow within this structure is successfully captured by a few POD eigenfunctions. Phase-space plots further indicate the existence of low-dimensional dynamics within the central channel. This conclusion supports the validity of a reduced-order model for fluidized beds, which can then be constructed by projecting the governing equations onto the POD modes, as it is commonly done in the Galerkin method. 2003 Elsevier Ltd. All rights reserved.