“…Interphase drag models Bed type Guo et al (2021) (Guo et al, 2021) Gidaspow (Gidaspow, 1994) (TFM and CFD-DEM), Single-spout Beetstra et al (Beetstra et al, 2007), Koch and Hill (Hill et al, 2001) and O'Brien, 1987) Chen et al (2019) (Chen et al, 2019) Syamlal O'Brien (Syamlal and O'Brien, 1987) (TFM) and Multiple-spout DeFelice (Di Felice, 1994) (CFD-DEM) Almohammed et al (2014) (Almohammed et al, 2014) Gidaspow (Gidaspow, 1994), Wen and Yu (Wen, 1966), Single-spout Syamlal O'Brien (Syamlal and O'Brien, 1987) (TFM) and Koch and Hill (Hill et al, 2001 closures of frictional solids stresses in the literature (Zhao et al, 2021;Guo et al, 2021;Wang et al, 2014;Zhao et al, 2022) such as Johnson and Jackson (Johnson and Jackson, 1987), Srivastava and Sundaresan (Srivastava and Sundaresan, 2003) and Syamlal et al (Syamlal et al, 1993) strongly depend on empirical parameter of minimum solids volume fraction, a min s (the point, where frictional stresses become non-negligible), and are monotonically increasing functions with increasing solids volume fraction. In addition, particle-wall impacts in these TFM simulations are resolved with Johnson and Jackson (Johnson and Jackson, 1987) boundary condition.…”