We investigated the influence of design parameters and operational conditions on lateral solid mixing in fluidized beds adopting the Eulerian-Eulerian modeling approach. To quantify the rate at which solids mix laterally, we used a lateral dispersion coefficient (Dsr). Following the usual approach employed in the literature, we defined Dsr by means of an equation analogous to Fick[U+05F3]s law of diffusion. To estimate Dsr, we fitted the void-free solid volume fraction radial profiles obtained numerically with those obtained analytically by solving Fick[U+05F3]s law. The profiles match very well. Our results show that Dsr increases as superficial gas velocity and bed height increase; furthermore, it initially increases with bed width, but then remains approximately constant. The values of Dsr obtained numerically are larger than the experimental ones, within the same order of magnitude. The overestimation has a twofold explanation. On one side, it reflects the different dimensionality of simulations (2D) as compared with real fluidized beds (3D), which affects the degrees of freedom of particle lateral motion. On the other, it is related to the way frictional solid stress was modeled: we employed the kinetic theory of granular flow model for the frictional solid pressure and the model of Schaeffer (1987) for the frictional solid viscosity. To investigate how sensitive the numerical results are on the constitutive model adopted for the frictional stress, we ran the simulations again using different frictional models and changing the solid volume fraction at which the bed is assumed to enter the frictional flow regime (ϕmin). We observed that Dsr is quite sensitive to the latter. This is because this threshold value influences the size and behavior of the bubbles in the bed. We obtained the best predictions for ϕmin=0.50. The results show that accurate prediction of lateral solid dispersion depends on adequate understanding of the frictional flow regime, and accurate modeling of the frictional stress which characterizes it
We model the stable expansion in gas-fluidized beds of different diameters. We solve the model and analyze the results using the Richardson and Zaki equation. We study the role of enduring particle-particle contacts in uniform gas-fluidized beds. We study the role of wall friction in uniform gas-fluidized beds. We conduct fluidization/defluidization experiments to validate our theoretical results. a b s t r a c tThe Richardson and Zaki (1954, Sedimentation and fluidization. Trans. Inst. Chem. Eng. 32, pp. 35-53.) equation has been used extensively to investigate the expansion profiles of homogeneous gas-fluidized beds. The experimental value of the parameter n appearing in the equation indicates how significantly interparticle forces affect the expansion of these beds, revealing the relative importance of these forces with respect to the fluid dynamic ones. In this work, we modeled the stable expansion of gas-fluidized beds of different diameter, accounting for enduring contacts among particles and wall effects. We solved the model numerically to obtain the bed expansion profiles, back-calculating from them the values of the parameter n. For all the cases considered, we observed that the values of n are higher than those obtained by purely fluid dynamic correlations, such as those advanced by Richardson and Zaki, and Rowe (1987, A convenient empirical equation for estimation of the Richardson and Zaki exponent. Chem. Eng. Sci. 42, pp. 2795.). This effect was more pronounced in beds of smaller diameter. To validate our model, we carried out fluidization and defluidization experiments, analyzing the results by means of the Richardson and Zaki equation. We obtained a reasonable agreement between numerical and experimental findings; this suggests that enduring contacts among particles, which are manifestations of cohesiveness, affect homogeneous bed expansion. This effect is amplified by wall friction.
We investigated lateral solid mixing in gas-fluidized beds using CFD and DEM. We ran 3D CFD simulations, comparing the results with those formerly obtained in 2D CFD simulations. We observed that the frictional stress model affects the numerical results. This was also observed in 2D simulations, but in 3D simulations the effect is less pronounced. The 3D simulations described the lateral solid mixing process more accurately than the 2D simulations, simulation dimensionality being an important factor. To analyse further the role of frictional stress models, we ran 3D DEM simulations, employing the soft-sphere approach to model the particle-particle contact forces. The simulation results agreed reasonably well with the empirical data, but their accuracy depended on the values used for the collision parameters; also, the 3D CFD simulations matched the empirical data more closely.Altogether, we concluded that the simulation dimensionality plays the dominant role in predicting lateral solid mixing accurately.
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