Further development of an energy-minimization multiscale modeling approach to simulating two-phase flow under turbulent conditions that considers the size distribution of mesoscale structures, i.e. bubbles and clusters, is presented. User-defined values of minimum and maximum cluster or bubble diameters were specified. A uniform size distribution was first considered as a test case, in which the drag force comprised contributions from each size group. The mathematical form of the objective function describing the energy for suspension and transport was not altered. The heterogeneity index of this new drag modification was then used to simulate pilot-scale circulating fluidized-bed risers involving Geldart group A particles. The results were validated against available experimental data. The model is capable of capturing both axial and radial profiles of flow-field variables.

提出了进一步发展能量最小化多尺度建模方法，以模拟湍流条件下的两相流动，该方法考虑了中尺度结构（即气泡和团簇）的尺寸分布。指定了用户定义的最小和最大簇或气泡直径值。首先将均匀的大小分布视为一个测试案例，其中阻力包括每个大小组的贡献。描述悬浮和运输能量的目标函数的数学形式没有改变。然后，使用这种新型阻力改进剂的异质性指数模拟涉及Geldart A组颗粒的中试规模循环流化床立管。根据可用的实验数据验证了结果。