Determining granular behavioural zones in rotating tumblers

The wide range of behaviour exhibited by granular flows has made them challenging to handle practically. For example, rotary mills used for grinding mining materials operate in the cataracting regime, which combines the whole range of flowing conditions for granular materials, including solid body motion, dense flow, and gaseous collisional regime. A good understanding of the material behaviour in such processes is crucial to optimise industrial operating conditions; however, this is rendered difficult by the large scales of the operations and the complexity of probing the charge inside the mills. In this paper, we present a method allowing for both comprehensive and manageable understanding of the local granular material behaviour, applicable to a wide variety of situations. Inspired by the example case of rotary mills, we perform discrete element numerical simulations of a rotating tumbler with lifters and extract the local fields of interest, such as strains, pressures, and density, through standard coarse-graining methods. Those smooth fields are then appropriately non-dimensionalised, and used as input for a clustering algorithm. The clustering allows pinpointing of distinct zones of behaviour in the tumbler. Crucially, those zones have well-identified physical properties, and are relevant to the whole range of rotation rates. These zones allow us to numerically study how the flow is affected by changes in operating conditions, similar field measurements in industry operating conditions are difficult to acquire due to the opacity of the mill and the harsh environment. We complement the numerical analysis by in-situ measurements in a laboratory scale three-dimensional rotating tumbler. We use recent technological advances in embedded sensors and X-ray dynamic radiography reconstruction to provide new insights into the behaviour of rotary mills, measuring particle trajectories and accelerations directly inside the mill. The analysis and experimental methods presented provide new tools and insights to analyse complex granular flows. They apply to the full range of granular regimes, and can be extended to a broad range of geometries and processes.