A Review of the Continuum Theory-Based Stress and Drag Models in Gas-Solid Flows

The continuum theory-based models, which include solid stress models and gas-solid drag models, are required for the modeling of gas-solid flows in the framework of the Eulerian–Eulerian method. The interactions among particles are characterized by their diverse behaviors at different flow regimes, including kinetic motion, particle–particle collision and enduring friction. It is difficult to describe the particle behaviors at various regimes by mathematical methods accurately. Therefore, it is very important to develop proper solid stress models that can capture the inherent characteristics of the flow behaviors. In addition, the gas-solid fluidization system is a typical heterogeneous system, which exhibits locally inhomogeneous structures such as bubbles or particle clusters with different shapes and sizes. Due to these inhomogeneous characteristics, the gas-solid drag model has become one of the key challenges in the simulation of gas-solid flows. Various forms of constitutive relations for solid stress models and gas-solid drag models have been reported in the literature. In this paper, we reviewed the solid stress models crossing various flow regimes and drag models in both micro- and mesoscales, which provide a useful reference for model selection in simulating gas-solid flows.