A second‐order moment method applied to gas–solid risers

Abstract

Second‐order moment method of particles is proposed on the basis of the kinetic theory of granular flow. Closure equations for the third‐order velocity moments are presented to account for the increase of the probability of collisions of particles on the basis of the elementary kinetic theory and order of magnitude analysis. The boundary conditions for the set of equations describing flow of particles are proposed with the consideration of the momentum exchange by collisions between the wall and the particles. The distributions of velocity, concentration and moments of particles are predicted. Simulated results are compared with experimental data measured by Tartan and Gidaspow and Bhusarapu et al. in risers, and Tsuji et al. in a vertical pipe. The effects of the closure equations for the third‐order velocity moments and the fluid‐particle velocity correlation tensor on flow behavior of particles are analyzed. © 2012 American Institute of Chemical Engineers AIChE J, 2012

Analysis of SO2 and NOx Emissions Using Two-Fluid Method Coupled with Eddy Dissipation Concept Reaction Submodel in Circulating Fluidized Bed Combustors

“…On the basis of the SOM model for gas–solid flow simulations, the SOM of particles equations are presented for the gas–solid reacting flow. The governing equations and the species equation of particles are given as follows: ∂ ∂ t ( α s ρ s ) + ∂ ∂ x i ( α s ρ s u s i ) = S sg ∂ ∂ t ( α s ρ s u s , i ) + ∂ ∂ x j ( α s ρ s u s i u s j ) = prefix∑ l = 1 N [ χ ( m s C i ) l …”

“…SOM of Particles Model. On the basis of the SOM model for gas−solid flow simulations, 24 the SOM of particles equations are presented for the gas−solid reacting flow. The governing equations and the species equation of particles are given as follows: …”

“…The EDC model is developed for combustion process in CFB combustors. For the particles-phase in the framework of two-fluid model, the kinetic theory of granular flow is widely adopted for closure. − The velocity fluctuations of particles show a clear discrepancy at each direction in CFB combustors, hence the SOM model based on KTGF is employed to consider the anisotropic behavior of particles …”

Direct comparison of Eulerian–Eulerian and Eulerian–Lagrangian simulations for particle‐laden vertical channel flow

“…Modeling particle‐laden flows is of major interest in developing a better understanding of these systems and, in an industrial context, improving process optimization, troubleshooting, and scale‐up. There has been a variety of approaches to modeling these systems including direct numerical simulation (DNS), Eulerian–Lagrangian (EL) simulation, and Eulerian–Eulerian (EE) simulation 1‐7 . One major challenge in doing so involves not only successfully resolving the features present but also doing so in a way that is computationally feasible and efficient 8,9 .…”

“…There has been a variety of approaches to modeling these systems including direct numerical simulation (DNS), Eulerian-Lagrangian (EL) simulation, and Eulerian-Eulerian (EE) simulation. [1][2][3][4][5][6][7] One major challenge in doing so involves not only successfully resolving the features present but also doing so in a way that is computationally feasible and efficient. 8,9 With that in mind, the purpose of this study is to evaluate the ability of an EE-anisotropic Gaussian (EE-AG) model [10][11][12] to reproduce the results of particle-laden channel flow modeled using an EL model.…”