Dense granular flows in rotating drums: A computational investigation of constitutive equations

Abstract

Novel 3D measures of compressibility and isotropy (coaxiality and collinearity) are proposed to test constitutive laws of rotating drum flows using the DEM with the μ(I) rheology is tested. The coaxiality measure produces a lower occurrence frequency than the equivalent 2D simulation for nearly all angular separations, while the collinearity measure shows minimal deviation. The high degree of isotropy is facilitated by compressibility across the gravity-driven, flowing layer, and a non-zero volumetric component of the velocity gradient tensor near the bottom of the densely-packed rising en-masse layer. 3D simulations facilitate compressibility which ultimately leads to better regularisation of the equations. An empirically-derived friction law produces statistically better fits when compared to several other friction laws proposed in the literature; however, all models fail to capture the behaviour at very low inertial numbers. The failure suggests gross instability in the governing equations which is the signature of ill-posedness and/or shear banding.