Mathematical Modeling and Pointwise Validation of a Spouted Bed Using an Enhanced Bed Elasticity Approach

Abstract

With a Euler–Euler (E2P) approach, a mathematical model for predicting the pointwise hydrodynamic behavior of a spouted bed was implemented though computational fluid dynamics (CFD) techniques. The model considered a bed elasticity approach in order to reduce the number of required sub-models to provide closure for the solids stress strain-tensor. However, no modulus of elasticity sub-model for a bed elasticity approach has been developed for spouted beds, and thus, large deviations in the predictions are obtained with common sub-models reported in literature. To overcome such a limitation, a new modulus of elasticity based on a sensitivity analysis was developed and implemented on the E2P model. The model predictions were locally validated against experimental measurements obtained in previous studies. The experimental studies were conducted using our in-house developed advanced γ-ray computed tomography (CT) technique, which allows to obtain the cross-sectional time-averaged solids holdup distribution. When comparing the model predictions against the experimental measurements, a high predictive quality for the radial solids holdup distribution in the spout and annulus regions is observed. The model predicts most of the experimental measurements for different particle diameters, different static bed heights, and different inlet velocities with deviations under 15%, with average absolute relative errors (AARE) between 5.75% and 7.26%, and mean squared deviations (MSD) between 0.11% and 0.24%

Pairing Experimental and Mathematical Modeling Studies on Fluidized Beds for Enhancement of Models Predictive Quality: A Current Status Overview

“…Some of the tested sub-models did not converge, such as when using the sub-model proposed by Uribe et al [49], which was expected, as this model was developed for a spouted bed. Among the modulus of elasticity tested, Figure 7 compares the submodels that led to the most accurate predictions of the local fields.…”

“…Numerical model of a spouted bed As suggested by Uribe et al [49] and show in Figure 2, the modulus of elasticity sub-models generally makes a strong contribution in the dense regions of the fluidized systems, and tends to zero as the beds get diluted. Hence, an additional pseudo-viscous contribution is included in the solids stress tensor approximation to model the solid-solid interactions in the diluted regions of the bed.…”

“…The second approach in modeling these systems is considering an Euler-Euler specification of the flow field, where both phases are treated as continuum interpenetrating phases, by considering the solid phase as a pseudo continuum phase [49]. This approach has been recognized as a promising alternative to the CFD-DEM models, as it allows to model large scale systems, while being computationally efficient, in terms of required computational resources and computing times [36,50].…”

“…The second alternative to model the solids stress tensor is the bed elasticity approach [64,65]. This approach, widely used in the early contributions on mathematical modeling of fluidization, is based on considering that the solid pseudo-phase behaves as an elastic body, which can be compressed and expanded [49]. The compression and expansion of the pseudo-phase is considered to be reflected in changes to the solid holdup (ε σ ).…”

“…Using the definition of Equation ( 22), a modulus of elasticity (−G(ε β )) is defined, which captures the changes in the solids stress tensor with respect to the changes in the local gas holdup ε β . Several moduli of elasticity have been proposed, generally for fine particles [66][67][68][69][70], and follow the generalized form described in Equation (23) [49,71,72].…”