MODELING OF MESO-SCALE STRUCTURES IN PARTICLE-FLUID SYSTEMS: THE EMMS/CFD APPROACH

Ning; Yang; Wei; Wang; Wei; Ge; Jinghai; Li

摘要

Meso-scale structures existing in the form of particle-rich clusters, streamers or strands in circulating fluidized beds, and of ascending bubble plumes and descending liquid-rich vortices in bubble columns and slurry-bed reactors, as commonly observed, have played an important role in the macro-scale behavior of particle-fluid systems. These meso-scale structures span a wide range of length and time scales, and their origin, evolution and influence are still far from being well understood.Recent decades have witnessed the emergence of computer simulation of particle-fluid systems based on computational fluid dynamic (CFD) models. However, strictly speaking these models are far from mature and the complex nature of particle-fluid systems arising from the meso-scale structures has been posing great challenges to investigators. The reason may be that the current two-fluid models (TFM) are derived either from continuum mechanics by using different kinds of averaging techniques for the conservation equations of single-phase flow, or from the kinetic theory of gases in which the assumption of molecular chaos is employed, thereby losing sight of the meso-scale heterogeneity at the scale of computational cells and leading to inaccurate calculation of the interaction force between particles and fluids. For example, the overall drag force for particles in a cell is usually calculated from the empirical Wen & Yu/Ergun correlations,which should be suspected since these correlations were originally derived from homogeneous systems.Schemes to solve this problem for gas-particles systems may be classified into four categories. First, one could capture the detailed meso-scale structure information at the cell scale by employing the so-called direct numerical simulation (DNS) (Hu, 1996), the pseudo-particle modeling (PPM) (Ge & Li, 2003), or the Lattice-Boltzmann method (LBM) to track the interface between gas and particles. Second, refinement of the computational meshes may reduce the heterogeneity to some extent and may be capable of capturing some meso-scale heterogeneity though there still exists some argument about the physical rationalityof this approach such as the treatment of particle phase as a continuum while fining the meshes. Third, it is generally agreed that a cascade description, viz. extracting the closure correlations for TFM from microscopic simulations such as PPM and LBM (van der Hoef et al., 2004), can suggest a practical way to explore the multi-scale heterogeneity. Although the above three schemes are logical and fundamental, they are generally difficult to implement at present due to the complexity of the models or the enormous computational cost. The fourth scheme we adopted in this study is the so-called energy-minimization multi-scale (EMMS) model which seems to be a simple yet reasonable approach at the moment.In the present approach, a "structure" model is established to describe the meso-scale heterogeneity through the definition of eight "structure parameters" and the resolution of structure involving a particle-rich dense cluster phase and a gas-rich dilute phase. Gas-solid interaction is also resolved into that between gas and particles inside both the dense cluster phase and the dilute phase, and that between the cluster phase and the dilute phase. This means that the drag force for the dense cluster phase includes two parts, namely, bypassing drag (ki) and permeating drag (kc) as depicted in Fig.1. We found that the absolute value of the difference (△k) between kc and ki could be employed to evaluate the extent of the system heterogeneity. On the basis of this structure model, the average acceleration (a) induced by gas-solid interactions can be obtained, and then the average drag coefficient (β) for the two-fluid model can be calculated. Calculation results show that the computed value ofβwith the EMMS model is much less than that with the Wen & Yu/Ergun correlations, which is in reasonable agreement with conclusions derived from experiments. We further simplified this model by assuming that the dense phase voidage (εc) is a constant because the direct incorporation of this new model into the two-fluid model is difficult at present due to computational cost resulting from the iterative process and certain limitations of this model stemming from its original derivation from the global fluidized bed system. With the Ug and Gs for the global system as the input parameters, we can calculateβfor each specified ε and thereby obtain the correlation of correction factor ω(ε) as a function of ε. Implanting this correlation into each cell and employing the local slip velocity and voidage, βfor each cell can thus be obtained.The simulation is performed for a FCC riser by combining the two-fluid model with this EMMS-based drag model and the Wen & Yu/Ergun correlations respectively. Comparison of the simulation results shows that the EMMS-based drag model produces more reasonable results than the Wen & Yu/Ergun correlations. The former shows its improvement in predicting the solids entrainment rate, the meso-scale heterogeneous structure involving clusters or strands, and the radial and axial voidage distributions. For the latter, the simulated flow structure is homogeneous and no clusters are observed, and the predicted solid entrainment rate is too much larger than experimental measurements. We also employ different approaches to predict the occurrence of choking, indicating that this EMMS-based drag model has the ability to capture this important phenomenon in CFB systems. For the details, the interested reader is referred to the work of Li and Kwauk (1994), and Yang et al. (2003a; 2003b; 2004; 2005).

MODELING OF MESO-SCALE STRUCTURES IN PARTICLE-FLUID SYSTEMS: THE EMMS/CFD APPROACH

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