Unification of EMMS and TFM: structure-dependent analysis of mass, momentum and energy conservation

Abstract

The two-fluid model (TFM) has been widely applied in simulation of various multiphase flow systems. In particular, for fine-particle circulating fluidization, the drag force plays a critical role whereas the classic drag models based on empirical correlations of homogeneous fluidization are found inadequate. Therefore, various approaches have been proposed in recent years to account for the effects of meso-scale structure on the drag force, in which the energy-minimization multi-scale model (EMMS) has received rapidly growing applications.However, the relationship between the TFM and EMMS has not been clarified to enable their combination. To solve this problem, we present a structure-dependent analysis of mass, momentum and energy conservation equations. This analysis is rooted in the structure-dependent multi-fluid model (SFM), which details the composition of drag forces and energy consumptions and their relationships with consideration of meso-structures. With assumption of homogeneous structures, it reduces to the TFM equations; for steady-state systems with structures, it restores the force balance equations, equal pressure drop relation and energy relationship of the EMMS. In future, the scale dependence of this analysis deserves more efforts to understand the applicability of the EMMS stability condition on different scales.