Drag Model Modifications for Gas-Solids Two-Phase Flows with Clusters in Circulating Fluidized Bed Risers

CFD modeling has been considered as an effective tool for researchers to design and study the multiphase flows inside circulating fluidized bed (CFB) risers. The Eulerian-Eulerian two-fluid method (TFM) is widely applied into simulations of gas-solids CFB risers. However, there are always discrepancies between the numerical results and the experimental data. The main reason might be the inaccurate drag models used between the gas and solids since single particles tend to agglomerate to clusters in the gas-solids CFB riser. The cluster usually consists of a group of single particles, so that it has higher solids concentration than the surrounding gas-solids suspension. The intensive gas-solids interactions result in the continuous formation and breakup of particle clusters in the CFB riser. When it comes to CFD modelling on the gas-solids flow in the CFB riser, the dynamic nature of the clusters makes it difficult to derive an accurate correlation for the drag force between the gas and solids phases.

Researchers have put a lot of effort to the modification of the drag models to include the cluster effect and all the current drag models that include the cluster effect can be generally classified into three groups based on different theories. In the first group, the drag models were modified based on the pressure drop data from the packed beds to include the cluster effect, such as Wen and Yu model, Gidaspow model, and Huilin-Gidaspow model. In the second group, drag model modifications were obtained based on the concept of the Richardson-Zaki equation, but with a correlated Vr based on the multiparticle system, such the popular used Syamlal-OIn both groups, the properties of single particle were used in the modified drag models. In the third group, the meso-scale heterogeneity theory of gas-solids system was used to modify the drag model, such as EMMS model and CSD model. Although “numerical” clusters were calculated based on the minimum energy dissipation theory form EMMS/CSD model, it has not been validated that those “numerical” clusters are the same as those real clusters existing in a fluidized bed.

Because of lacking experimental data on clusters, most of the modified drag models try to include the cluster effect by adding a factor to the drag models developed for the uniformly distributed particles, However, the properties of single particles were still used in those modified drag models. Some of those modified drag models work well under certain flow conditions in fluidized beds, but they are not suitable for general cases. A general drag model that includes the cluster effect in gas-solids fluidization systems is developed in this study based on the statistical data of the clusters with the help of image analytical experiments.

The drag model including the clustering effect

There are two types of clusters in CFB riser: one is “core” cluster in which particles are tightly packed by the fluid and can be hardly breakup when rising along the riser; another is “cluster of core clusters” which are many loosely aligned “core” clusters and they are frequently formed and breakup inside the CFB riser. With the help of the experimental data, the statistical results of the diameter and density of the “core” clusters can be obtained from the image analysis. The solids in a CFB riser can be divided into a cluster phase which consists of “core” clusters and a single particle phase which only contains individual particles. Therefore, the drag force between gas and solids phases in CFD simulations can be determined from the summation of the drag force between the cluster phase with the cluster properties and the gas phase, and the drag force between the single particle phase and gas phase.

The Sparsely Distributed Solid Particles drag model (Schiller & Naumann) is used for the calculations of the drag force for both the cluster phase and single particle phase, but with different input parameters for those two phases. . When calculating the drag force for the cluster phase, the clusters are assumed as stable spheres (“core” clusters) with a constant diameter, d_cl and density, , based on statistical data from the experiments. The volume fraction of the clusters phase is also defined from the statistical data by the image analysis. The slip velocity of the clusters is assumed based on different operating conditions.The effects of the cluster relaxation time and the surrounding solids holdup are also considered and compared by two other cases in the results section to better present the effectiveness of the proposed cluster drag model.

Three CFD cases as shown in Tab. 1 are setup to compare the cluster-driven drag model and the commonly used Syamlal and O'Brien drag model in TFM method. A typical operating condition of Ug = 5m/s, Gs = 100 kg/m²s for FCC particles in the CFB riser is selected for numerical simulation. The corresponding statistic data for the cluster properties under the same operating condition are: cluster diameter, d_cl = 0.0058m, cluster density is 0.052, and cluster phase volume fraction to the solids phase is 0.5.

Table 1: Cases setup details

Results and discussion

The overall solids holdup profiles form Case #1-3 do not have much difference between the commonly used Syamlal and O'Brien drag model and the proposed drag model and they both have a slight deviation from the experimental data. The overall solids velocity profiles show that Case #2 overestimated the particle velocity compared with Case #3 because the effects from cluster relaxation time and surrounding solids holdup are not included. However, there is almost no difference among Case #1 and Case #3, which indicates that the impacts from cluster relaxation time and the surrounding solids holdup are not as significant as the cluster size and density. More details will be provided in the full paper.

Conclusions

A new drag model which includes the cluster effect is proposed in this work. With the help of the image analysis, the statistical data from the experiments for the properties of the clusters such as the cluster diameter, density, and its total volume fraction of the solids phase are employed in the proposed drag model. The total drag force then can be determined by the summation of the drag force between cluster phase and gas phase, and the drag force between the single particle phase and gas. Although the overall flow structures don not have a significant difference between the proposed drag model and the commonly used drag model, the flow details did reflect the impacts of the clusters on the drag force. More frequent clustering phenomenon can be found in the numerical results by the proposed drag modification, which indicates the advantage and accuracy by implementing the cluster properties into drag model although more detailed future work needs to be done.