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To consider the critical effect of mesoscale structure on the drag coefficient, this paper presents a drag model based on the energy-minimization multiscale (EMMS) approach. The proposed structure parameters are obtained from the EMMS model, and then the average drag coefficient can be calculated from the structure parameters and further incorporated into the two-fluid model to simulate the gas−solid flow in a circulating fluidized-bed riser. Simulation results indicate that the simulated flow structures are different for the EMMS-based drag model and the hybrid model using the Wen and Yu correlation and the Ergun equation. The former shows its improvement in predicting the solids entrainment rate, the mesoscale heterogeneous structure involving clusters or strands, and the radial and axial voidage distributions. The simulation results support the idea that the average drag coefficient is an important factor for the two-fluid model and suggest that the EMMS approach could be used as a kind of multiscale closure law for drag coefficient.
Yang et al. (Tue,) studied this question.