Abstract
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׳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׳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.
Highlights
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 in fluidized beds, researchers often resort to axial and lateral dispersion coefficients; these, as we shall see in this study, are effective diffusivities relating to the times that solids take to spread axially and laterally over a given distance in the bed
We investigated the effect of bed height on lateral dispersion coefficients
Summary
We investigated the influence of design parameters and operational conditions on lateral solid mixing in fluidized beds adopting the Eulerian-Eulerian modeling approach. Kashyap and Gidaspow (2011) summarized these methods as saline (Rhodes et al, 1991), ferromagnetic (Avidan and Yerushalmi, 1985), thermal (Borodulya and Epanov, 1982), radioactive (Mostoufi and Chaouki, 2001), carbon (Winaya et al, 2007) and phosphorescent (Du et al, 2002) tracing methods These experimental approaches have their limitations: in thermal tracking techniques heat is transferred to the fluid phase and walls, making it difficult to interpret the results; in radioactive tracking methods safety of equipment and personnel are of great concern; in phosphorescence tracking methods most successful applications usually take place in dilute fluidized beds. Experiments with solid tracers are difficult to perform because of lack of continuous sampling and presence of residual tracer Despite these experimental investigations, the understanding of how design parameters and operating conditions affect lateral dispersion coefficients is still limited, because the mechanisms governing solid mixing are complex
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