采用两步法将气泡EMMS模型拓展到计算网格层次，用于模拟鼓泡床两相流动，改进的EMMS曳力模型不仅与空隙率有关，且与网格内的速度直接关联. 求解是在操作条件下利用宏观稳定性约束条件寻优得到乳化相内空隙率关系式，再用计算网格层次上的微观守恒方程结合乳化相空隙率关系式封闭求解其余结构参数及对应的曳力系数，最后借助用户自定义函数将气泡EMMS曳力嵌入双流体模型中，对含Geldart A类颗粒的鼓泡床内气固两相流动行为进行模拟与验证. 结果表明，该模型能较好地模拟鼓泡床内的非均匀流动结构，准确捕捉到上稀下浓的轴向颗粒浓度分布特征，轴向颗粒浓度分布结果与实验值较接近，平均相对偏差为6.4%. 床层径向上颗粒分布均呈明显的环?核结构. 在不同床层高度(0.6, 0.8和1.1 m)处的径向颗粒浓度分布与实验值基本吻合，仅在底部(0.4 m)略低，相对偏差小于14%. 而Gidaspow曳力模型在4个床层高度与实验数据差距甚远，相对偏差可达91%.

For simulation of gas?solid bubbling fluidized bed, the bubble-based energy minimization multi-scale (EMMS) model was extended to the sub-grid level through a two-step scheme. The modified EMMS drag is not only related to the voidage, but also associated with velocities within a computing grid. For a specified operating condition, the emulsion voidage was obtained under the optimization of a macro-level stability condition. Then the structure parameters and corresponding drag coefficient were solved by a set of conservation equations with the emulsion voidage correlation at the sub-grid level. Finally, this new drag was coupled with the two-fluid model (TFM) through a user-defined function (UDF) to simulate bubbling fluidized bed with Geldart A particles. It was shown that this new drag could well describe heterogeneous flows of bubbling fluidized beds and reasonably predict the axial profile of average solid concentration with a dilute-top and dense-bottom distribution. The values of axial average solid concentration are close to the experimental data with a relative deviation of 6.4%. Obviously, the radial solid concentration has higher value near the wall than at the center, showing good agreement with experiment at different heights (0.6, 0.8 and 1.1 m) except at the bottom (0.4 m) with a relative deviation of less than 14%. By comparison, the Gidaspow drag model underestimates radial solid concentration with a relative deviation of 91% at four bed heights.