Experimental and numerical description of rapid granular flows and some baseline constraints for simulating 3-dimensional granular flow dynamics

Abstract

Accurate prediction of rapid granular flow behavior is essential to optimize protection measures from hazardous natural granular flows like snow avalanches and landslides and to design efficient production facilities for granulate processing industries.<br /> So far, most successful models for rapid granular flow descriptions employ depth-averaging, assuming an essentially constant velocity over depth. This assumption greatly reduces calculation power but can lead to incorrect predictions in regions of strong velocity shearing in the flow depth direction, e.g., during the impact on an obstacle. To overcome these limitations, this study introduces a novel type of non-depth-averaged fluid dynamics simulations for rapid granular flows of cohesionless material. A series of small scale experiments with industrial (polyvinyl chloride (PVC)) and natural (sand) granular material was performed (i) to select and refine the appropriate rheological model, (ii) to yield a better insight into velocity profiles and (iii) to obtain parameters for comparison with numerical simulations. Based on these experiments, Coulomb-type friction was selected as rheological model. A Poly(methyl methacrylate) channel set-up with variable inclination angle in combination with high-speed image recording and an open source particle image velocimetry (PIV) software developed in this study allowed detailed observation of velocity profiles during flow inception, undisturbed flows, flows encountering obstacles, and shock scenarios. The PIV measurements revealed considerable changes in velocity between layers of the granular flow and thus underpin the necessity to perform non-depth-averaged simulations in order to accurately describe the flow behavior in all aspects. Comparison of the depth-averaged simulation model of the Savage-Hutter type and the non-depth-averaged simulation method introduced here with the experiments revealed that certain quantities, like the flow height and shape could only be accurately predicted using the non-depth-averaged simulations. Furthermore, the non-depth-averaged simulations were well capable of predicting the observed velocity profiles and produce accurate predictions of associated quantities like strain rates and slip velocities for both materials in most experiments. <br /> Nevertheless, this study also revealed cases where both depth-averaged and non-depth-averaged methods generate similar predictions, e.g., the height of an undisturbed flow and deposition shapes. A detailed summary of parameters and dynamic variables in different experiments, and their predictability by both methods is provided. This serves as a guideline to decide when to employ the reduced but faster depth-averaged methods and when more calculation power intensive, but more accurate, non-depth-averaged methods must be employed. The non-depth-averaged method developed in this study was further validated to measure its predictive power in three dimensional experiments with obstacles. Also here, accurate predictions were observed. Furthermore, a method for the introduction of complex topographies into the simulation process was developed, allowing the direct integration of real mountain topographies. As pilot tests, simulations of granular flows on a complex experimental topography and a real case snow avalanche described in the literature were performed. The results demonstrated that the new method can be transferred to complex topographies and yields good predictions. These findings can serve as a basis for further refinement of the model and its expansions to describe more complex events, e.g., the entrainment of snow mass.<br /> Taken together, the novel, non-depth-averaged model and simulation technique build in this study based on the experimental observation are a suitable tool to predict important flow dynamical quantities in non-cohesive granular flows of both natural and industrial origins. Furthermore, it can serve as a basis for the development of a non-depth-averaged predictive model for real scale hazardous granular flows and is thus an important step towards the correct prediction of granular flow behavior for risk assessment in endangered regions.