Two-Fluid Simulation of a Three-Dimensional Spout-Fluid Bed: Flow Structures, Regimes, and Insight into the Mechanism of Particle–Particle Momentum Transfer

Abstract

Spout-fluid beds are widely used in the process industry due to their facilitation of an efficient contact between particles and gas. In this paper, a two-fluid model (TFM) is set up to reproduce the various flow structures encountered during spout-fluid bed operation. The effects of normal restitution model and gas–solid drag model are assessed by comparing simulation results with the experimental and discrete particle modeling (DPM) data of Link et al. [Link et al. Chem. Eng. Sci. 2005, 60, 3425–3442; Link et al. AIChE J. 2008, 54, 1189–1202.]. Simulation results show that application of an effective restitution coefficient in TFM can improve the accuracy of prediction significantly. The drag model of HKL predicts a more reasonable result than models of Huilin-Gidaspow, BVK, and Syamlal and O’Brien. Analysis on relative contributions of kinetic motion, friction, and collision to particle–particle momentum transfer parameters, namely, particle pressure and viscosity, shows that particle–particle momentum transfer in the spout and fountain regions is dominated by kinetic motion and that in the annulus region is dominated by friction. A transition region between spout and annulus regions is proposed. This region can be delineated using a single parameter of dimensionless collisional particle pressure because in this region, particle pressure is dominated by the collisional contribution. With an increasing spout-fluid ratio, the stable spout–annulus–fountain structure gradually shifts to an unstable bubble–slug structure. The effect of collision increases and extends to the entire bed. Meanwhile, the effects of kinetic motion and friction decrease. When slugs are formed, a rebound in the influence of friction is observed, accompanied by a decrease in the influence of collision.

A comprehensive comparison of Two-Fluid Model, Discrete Element Method and experiments for the simulation of single- and multiple-spout fluidized beds

“…Interphase drag models Bed type Guo et al (2021) (Guo et al, 2021) Gidaspow (Gidaspow, 1994) (TFM and CFD-DEM), Single-spout Beetstra et al (Beetstra et al, 2007), Koch and Hill (Hill et al, 2001) and O'Brien, 1987) Chen et al (2019) (Chen et al, 2019) Syamlal O'Brien (Syamlal and O'Brien, 1987) (TFM) and Multiple-spout DeFelice (Di Felice, 1994) (CFD-DEM) Almohammed et al (2014) (Almohammed et al, 2014) Gidaspow (Gidaspow, 1994), Wen and Yu (Wen, 1966), Single-spout Syamlal O'Brien (Syamlal and O'Brien, 1987) (TFM) and Koch and Hill (Hill et al, 2001 closures of frictional solids stresses in the literature (Zhao et al, 2021;Guo et al, 2021;Wang et al, 2014;Zhao et al, 2022) such as Johnson and Jackson (Johnson and Jackson, 1987), Srivastava and Sundaresan (Srivastava and Sundaresan, 2003) and Syamlal et al (Syamlal et al, 1993) strongly depend on empirical parameter of minimum solids volume fraction, a min s (the point, where frictional stresses become non-negligible), and are monotonically increasing functions with increasing solids volume fraction. In addition, particle-wall impacts in these TFM simulations are resolved with Johnson and Jackson (Johnson and Jackson, 1987) boundary condition.…”

“…In addition, the validity of the derived constitutive closures for particle-particle interactions and particle-wall boundary conditions in TFM approach can be examined in modelling of the spout fluidized beds. There are extensive studies in the literature on the modelling of the spout fluidized beds with either CFD-DEM (Jajcevic et al, 2013;Link et al, 2005;Link et al, 2007;Link et al, 2008;van Buijtenen et al, 2009;Buijtenen et al, 2012;van Buijtenen et al, 2011;Yang et al, 2019;Yue et al, 2019;Yue et al, 2021) or TFM (Zhao et al, 2021;Wang et al, 2014;Wu et al, yyyy;Zhao et al, 2016;Zhao et al, 2022) approaches. For instance, Link et al (Link et al, 2005) investigated the CFD-DEM simulations of the single-spout fluidized beds in different flow regimes, and van Buijtenen et al (van Buijtenen et al, 2011) studied different flow regimes in the multiple-spout fluidized beds via experiments and CFD-DEM simulations.…”

“…Due to discrete nature of the CFD-DEM method, it can fully resolve the contacts in all regions, however in the TFM approach, closures are needed to sufficiently consider these interactions. In the commonly used TFM approach for modelling of the spout fluidized beds (Guo et al, 2021;Chen et al, 2019;Almohammed et al, 2014;Zhao et al, 2021;Wang et al, 2014;Wu et al, yyyy;Zhao et al, 2016;Zhao et al, 2022), interstitial fluid effect on the kinetic-collisional solids stresses and pseudo-thermal energy flux has been ignored while studies of Wartha et al (Wartha et al, 2022), Agrawal et al (Agrawal et al, 2001) and Schneiderbauer et al reveal its importance. Furthermore, conventional frictional solids stresses models based on Coulomb's law (Schaeffer, 1987;Syamlal et al, 1993;Johnson and Jackson, 1987;Johnson et al, 1990;Srivastava and Sundaresan, 2003;Benyahia, 2008) manifest order-zero dependence on the rate of deformation in the quasi-static granular regime and are suitable just for dense regimes (Van Wachem et al, 2001).…”

Experimental and Numerical Study of Cross-Domain Hydrodynamics in an Integrated Pneumatic-Spouted Bed

“…Wu et al studied 3D hydrodynamic behaviors of a spouted bed under swirling flow. Zhao et al reported that the application of an effective restitution coefficient and drag model in TFM method could improve the accuracy of prediction significantly in a 3D spouted fluidized bed. Furthermore, they simulated and studied the hydrodynamics and heat transfer of a 3D spouted–fluidized bed with single, double, and triple chambers …”