Simulation of gas–solid two-phase flow by a multi-scale CFD approach—of the EMMS model to the sub-grid level

Abstract

Gas–solid two-phase flow features temporal-spatial multi-scale structures. Calculation of characteristic scales for an air/FCC (fluid-catalytic-cracking particle) flow indicates that the lack of scale separation entails a structure-dependent modeling approach even on the sub-grid level. For solving this problem, the energy-minimization multi-scale (EMMS) model is extended and coupled with computational fluid dynamics (CFD) through calculation of a structure-dependent drag coefficient in each grid, for which the schemes EMMS/sub-grid and EMMS/matrix are presented. Numerical analysis of the extended EMMS model suggests that gas and particles tend to achieve a compromise of flow dominance by gas finding the way with less resistance and particles clustering. So the dilute-phase part of drag force can be neglected and the major flow resistance arises from inside the dense-phase aggregate and over the interface. The inertial difference between the dense phase and the interface results in breakup or formation of particle clusters. The integrated approach is further verified through numerical description of the choking point demarcating the flow regime transition between the dilute pneumatic transport and the all-dense flow. Simulation shows that usual practice with assignment of only gas velocity and solids flux is insufficient for determination of the dense bottom height in a riser, and this can be attributed to the absence of another independent variable, solids inventory or imposed pressure drop. This critical phenomenon has been identified by earlier experiments, but most simulation practitioners remain unaware of it. More verification of the model is performed through visualization of micro-scale dynamics, characterization of meso-scale clusters and quantification of macro-scale distribution of two-phase parameters. Good agreement with experimental evidence is quite encouraging even quantitatively.