On the Accuracy of the Energy Minimization Multiscale (EMMS) Model for Circulating Fluidized Beds

Coarse grid simulations of circulating fluidized bed (CFB) reactors require accurate predictions of the particle drag force. Conventional homogeneous drag laws are known to be insufficient for such configurations owing to the heterogeneous structure of the particles that emerges (e.g., clustering). The Energy Minimization Multi-Scale (EMMS) model has received much attention for capturing the effect of heterogeneity in simulations of CFB reactors. Originally derived for calculating the net particle force in CFB risers, EMMS has been integrated within coarse grid simulations of Euler-Euler (EE) and Euler-Lagrange (EL) approaches to modify the drag force in each computational cell.

The EMMS approach decomposes the flow field into a dense and dilute phase that interact with each other. Many assumptions are made in the derivation of this model including (i) heterogeneity is represented by a single spherical cluster; (ii) invariant gas and particle superficial velocities for each phase; (iii) constant void fraction for each phase; and (iv) invariant particle drag force within the phases, among others.

Leveraging highly resolved EL simulations, we present a critical assessment of the EMMS model. The fundamental assumptions are probed in detail and model accuracy is quantified. We consider two flow regimes (i) fully developed settling of inertial particles under gravity and (ii) fully developed particle-laden pipe flow, representing unbounded and wall-bounded regimes, respectively. The former mimics the individual computational cells in the coarse-grained EE or EL simulations to which the EMMS model is typically applied, while the latter resembles the original application of the EMMS model for fast fluidization regimes. A structure tracking algorithm is applied to the EL data to measure cluster characteristics. Results show significant variation in the two-phase flow parameters, unlike the single-value predictions of the EMMS model. This work can provide a framework for incorporating the observed variation and improving the EMMS model.