Comparative analysis of subgrid drag modifications for dense gas‐particle flows in bubbling fluidized beds

Abstract

Many subgrid drag modifications have been put forth to account for the effect of small unresolved scales on the resolved mesoscales in dense gas‐particle flows. These subgrid drag modifications significantly differ in terms of their dependencies on the void fraction and the particle slip velocity. We, therefore, compare the hydrodynamics of a three‐dimensional bubbling fluidized bed computed on a coarse grid using the drag correlations of the groups of (i) EMMS, (ii) Kuipers, (iii) Sundaresan, (iv) Simonin, and the homogenous drag law of (v) Wen and Yu with fine grid simulations for two different superficial gas velocities. Furthermore, we present an (vi) alternative approach, which distinguishes between resolved and unresolved particle clusters revealing a grid and slip velocity dependent heterogeneity index. Numerical results are analyzed with respect to the time‐averaged solids volume fraction and its standard deviation, gas and solid flow patterns, bubble size, number density, and rise velocities. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4077–4099, 2013

Towards accurate three-dimensional simulation of dense multi-phase flows using cylindrical coordinates

“…simulations using the cylindrical grid 18 × 120 × 12 (say, for the bubbling fluidization case) be compared with the Cartesian grid 15 × 120 × 15 (note: 15 diametrical cells). However, with this cross-sectional resolution, the resulting Cartesian grid is too coarse (25 times the particle diameter) and hence, cannot predict the hydrodynamics accurately [35,39]. On the other hand, a Cartesian grid with identical cross-sectional resolution as the cylindrical radial grid may be used, i.e.…”

“…The application of an appropriate centerline treatment, though, is still imperative and numerically, it particularly affects the computation of the diffusion and drag force terms in the cells at the grid center. Thus, using an accurate centerline condition is not only essential for understanding the hydrodynamics of more complex flows (eg mixtures, reactive flows) but also for constructing accurate sub-grid models for coarse grid simulations [33][34][35]. Recently, Verma et al [28] simulated solid-gas fluidization in a cylindrical bed using a similar approach and predicted the radial velocity using diametrical momentum averaging.…”

Numerical Study of a Bi-disperse Gas-solid Fluidized Bed Using an Eulerian and Lagrangian Hybrid Model

“…However, such a procedure inevitably neglects small (unresolved) scales, which leads, for example, to a considerable overestimation of the bed expansion in the case of fine particles. Many sub-grid drag modifications have, therefore, been put forth by academic researchers to account for the effect of small unresolved scales on the resolved meso-scales in this case [2,3,[14][15][16][17][18].…”

“…The main idea of such a modeling strategy is to use a combination of a Lagrangian discrete phase model (DPM) and a coarse-grained TFM to take advantage of the benefits of those two different formulations. Furthermore, sub-grid drag corrections [2][3][4] are applied to account for the impact of the small unresolved scales on the gas-solid drag force. As in our earlier studies [4,6] we use a coarse-grained kinetic-theory based two-fluid model to study fluidization.…”

Approaching virtual process engineering with exploring mesoscience

“…The model has also been subjected to extensive tests from outside and to various modifications to meet the requirements of the specific problems they studied. It has been modified (i) to simulate CFB combustors [114,115], calcium looping for CO 2 capture in a lignite fired power plant [116], CFB carbonator [117] and gas desulfurization in a CFB riser [118]; (ii) to address the anisotropic characteristics of EMMS drag model [119]; (iii) to test the effects of using different particle cluster size correlations [120,121]; (iv) to model the effective interphase drag force of bubbling fluidization [122][123][124]; (v) to formulate an EMMS drag model that is conceptually consistent with the so-called type A two-fluid model and its applications [125][126][127][128][129][130]; (iv) to formulate another version by assuming the particle in dilute phases are in dilute limit and the particles in dense phase satisfy the Richardson-Zaki correlation [131,132]. Recent studies have shown that the EMMS drag model can also be used in Eulerian-Lagrangian simulations [133][134][135][136][137].…”