Filtered and heterogeneity‐based subgrid modifications for gas–solid drag and solid stresses in bubbling fluidized beds

Abstract

Two different approaches to constitutive relations for filtered two-fluid models (TFM) of gas-solid flows are deduced. The first model (Model A) is derived using systematically filtered results obtained from a highly resolved simulation of a bubbling fluidized bed. The second model (Model B) stems from the assumption of the formation of subgrid heterogeneities inside the suspension phase of fluidized beds. These approaches for the unresolved terms appearing in the filtered TFM are, then, substantiated by the corresponding filtered data. Furthermore, the presented models are verified in the case of the bubbling fluidized bed used to generate the fine grid data. The numerical results obtained on coarse grids demonstrate that the computed bed hydrodynamics is in fairly good agreement with the highly resolved simulation. The results further show that the contribution from the unresolved frictional stresses is required to correctly predict the bubble rise velocity using coarse grids.

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

“…For the numerical simulation we use the commercial CFD-solver FLUENT (version 14), whereby we implemented the poly-disperse drag force [20] and the coarse grained solid stresses of [2][3][4]23] by using user defined functions. For the discretization of all convective terms a second-order upwind scheme is used.…”

“…However, these previous studies did not include the impact of segregation. Since these models are well documented in our previous studies [2][3][4]6], we do not repeat the details here.…”

“…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].…”