Developing A Rheological Relation for Transient Dense Granular Flows Via Discrete Element Simulation in A Rotating Drum

This work examines the mu(I)relation that describes the effective friction coefficient mu of a dense granular flow as a function of flow inertial numberI, at the center of a rotating drum from its flow onset to steady state using DEM. We want to see how the internal friction coefficient of an accelerating flow may be predicted so that the associated tangential stress can be estimated with the proper knowledge of the normal stress. Under the three investigated drum speeds (3, 4.5 and 6 rpm), the bulk normal stress, sigma(n)(y), is found to be a consistent linear depth profile throughout the flow development with a slope degraded from the hydrostatic value, P-h(y), due to lateral wall friction. With the discovery of a non-constant depth-decaying effective wall friction coefficient, we derive analytically a wall-degradation factor K(h) to give sigma(n)(y) = K(h)P-h(y). The depth profile of tangential stress, however, varies in time from a concave shape upon acceleration, tau(a)(y), to a more linear trend at the steady state, tau(ss)(y). Hence, the mu(a)-I(a)profile (with mu(a)=tau/sigma(n)) upon flow acceleration offsets from the steady mu(ss)(I-ss) relation. A pseudo-steady acceleration modification number, Delta I, is proposed to shift the inertial number in the acceleration phase toI* = Ia+Delta I so that the mu(a)-I* data converge to mu(ss)(I-ss). This finding shall allow us to predict a transient tangential stress by tau(a)(y) = mu(ss)(I*)K(y)P-h(y) using the well-accepted knowledge of steady flow rheology, hydrostatic pressure, and the currently developed wall-degradation factor.