An EMMS-based multi-fluid model (EFM) for heterogeneous gas–solid riser flows: Part I. Formulation of structure-dependent conservation equations

In gas–solid riser flows, meso-scale structures have significant effects on the flow, mass/heat transfer as well as reaction behavior. To be consistent with these structures, this paper reformulates the Energy-Minimization Multi-Scale (EMMS) model in terms of its structure-dependent conservation equations. These conservation equations (namely the Structure-dependent multi-Fluid Model, SFM) may reduce to the Two-Fluid Model (TFM) if homogeneous distribution is assumed within each grid, and restore to the balance equations of the original EMMS model if they are used to describe steady-state, global behavior. The closure of the structure-dependent parameters in SFM requires the stability condition defined in the original EMMS model. Thus, the EMMS-based multi-Fluid Model (EFM) can be defined with the stability-constrained SFM. Our previous practice in Multi-Scale Computational Fluid Dynamics (MSCFD), which is characterized by coupling of TFM and EMMS drag coefficient, can then be viewed as a simplified realization of EFM. Finally, simulation with this simplified version of EFM was performed and compared to experimental data for verification.

► A structure-dependent multi-fluid model (SFM) is proposed for riser flows.
► The SFM reduces to the two-fluid model (TFM) for homogeneous flow.
► The SFM may restore to the energy-minimization multi-scale (EMMS) model.
► Solution of SFM with stability condition restores to coupling of TFM and EMMS.