A critical assessment of the Energy Minimization Multi-Scale (EMMS) model

Abstract

Coarse grid simulations of circulating fluidized bed (CFB) reactors require an accurate estimation of the particle drag force. Conventional homogeneous drag laws are known to be insufficient for such configurations owing to the tendency of particles to cluster. The Energy Minimization Multi-Scale (EMMS) model has received much attention in recent years for capturing heterogeneity in simulations of CFB reactors. In this paper, we critically review the EMMS model by revisiting the original formulation, underlying assumptions, key modifications, and improvements. Some capabilities as well as discrepancies of the model are explained along with areas for future improvements. Leveraging highly resolved Euler–Lagrange (EL) simulations, we present a critical assessment of EMMS and its fundamental assumptions. A fully-developed homogeneous flow of solid particles settling under gravity is considered as a test case. Strong inter-phase coupling results in the spontaneous generation of dense clusters that generate and sustain underlying turbulence. This setup is analogous to an individual computational cell within a coarse grid two-fluid model or EL simulation for which the EMMS model is typically applied. A structure tracking algorithm is applied to the EL data to identify clusters and measure their characteristics. Significant variation is observed in the two-phase flow parameters, in contrast with the key assumptions in the EMMS model. Variance-based sensitivity of the model parameters is performed to identify individual terms that contribute most to the EMMS prediction. This work provides a framework for incorporating the observed variation and improving the standard EMMS model.