A reduced-order model for heat transfer in multiphase flow and practical aspects of the proper orthogonal decomposition

This paper discusses two practical aspects of reduced-order models (ROMs) based on proper orthogonal decomposition (POD) and presents the derivation and implementation of a ROM for non-isothermal multiphase flow. The POD method calculates basis functions for a reduced-order representation of two-phase flow by calculating the eigenvectors of an autocorrelation matrix composed of snapshots of the flow. The flow is divided into transient and quasi-steady regions and two methods are shown for clustering snapshots in the transient region. Both methods reduce error as compared to the constant sampling case. The ROM for non-isothermal flow was developed using numerical results from a full-order computational fluid dynamics model for a two-dimensional non-isothermal fluidized bed. Excellent agreement is shown between the reduced- and full-order models. The composition of the autocorrelation matrix is also considered for an isothermal case. An approach treating field variables separately is shown to produce less error than a coupled approach. (C) 2012 Elsevier Ltd. All rights reserved.