Bubble size distribution resulted from bubble coalescence and breakup has significant effects on the effective interphase drag in gas-solid bubbling fluidized beds, which was however not taken into account in previous coarse-grid simulations. In this study, the population balance model (PBM) was used to describe the dynamic evolution of gas bubbles in gas-solid bubbling fluidization, wherein the coalescence and breakup kernels were derived by considering the effects of bubble velocity difference, wake capture and bubble instability. An improved energy-minimization multi-scale (EMMS) bubbling model was developed to calculate the effective interphase drag in sub-grid scale. By incorporating both the PBM and the EMMS drag into an Eulerian continuum model, a CFD-PBM-EMMS coupled scheme was further proposed to predict the hydrodynamics of bubbling fluidized beds. The scheme was validated through comparison of simulated results with experimental data. The bed expansion characteristics and the lateral profiles of solids velocities were reasonably predicted at acceptable computational cost. Satisfactory agreement was also achieved between the measured and simulated bubble size distributions. The proposed sub-grid drag model and coupled simulation scheme can facilitate capturing the salient features of the hydrodynamics of gas-solid bubbling fluidized beds.

由气泡聚结和破裂引起的气泡尺寸分布对气固鼓泡流化床中的有效相间阻力有显着影响，但是在以前的粗网格模拟中未考虑在内。在这项研究中，人口平衡模型（PBM）用于描述气固气泡流化过程中气泡的动态演化，其中考虑气泡速度差，尾流捕获和气泡不稳定性的影响得出聚结和破裂核。 。建立了改进的能量最小化多尺度冒泡模型，以计算子网格尺度下的有效相间阻力。通过将PBM和EMMS都合并到欧拉连续谱模型中，进一步提出了CFD-PBM-EMMS耦合方案来预测鼓泡流化床的流体动力学。通过将模拟结果与实验数据进行比较，验证了该方案。以可接受的计算成本合理地预测了床层膨胀特征和固体速度的侧向分布。在测量的气泡尺寸分布和模拟的气泡尺寸分布之间也取得了令人满意的一致性。提出的子网格阻力模型和耦合仿真方案可以方便地捕获气固鼓泡流化床水动力的显着特征。在测量的气泡尺寸分布和模拟的气泡尺寸分布之间也取得了令人满意的一致性。提出的子网格阻力模型和耦合仿真方案可以方便地捕获气固鼓泡流化床水动力的显着特征。在测量的气泡尺寸分布和模拟的气泡尺寸分布之间也取得了令人满意的一致性。提出的子网格阻力模型和耦合仿真方案可以方便地捕获气固鼓泡流化床水动力的显着特征。