Discrete Element Modeling of Granular Flows in Vibrationally-fluidized Beds

The main objective of the project was to develop a model for the motion of granular media under vibration in a tub vibrator. For such a system, it was decided that a discrete element method (DEM) was the most appropriate tool to model bulk velocity and circulation of media. In the first phase of the work, a vibratory finisher was modified to introduce planar vibration into a single layer of particles. The motion of the tub was measured using accelerometers and the corresponding granular media behavior was determined by video recording. A discrete element model, based on Cundall’s approach to contact, was developed to model granular flow in different vibratory beds, and the results were compared with experimental measurements of bulk flow velocity and bed expansion for the tub finisher. The sensitivity of the model predictions to the contact parameters was considered and the parameters were optimized with respect to the experimental results. After optimization, the difference between the model predictions of the bulk flow velocity and the measurements was less than 20% at four locations in media beds of two depths. The average bulk density of the vibrating beds was also predicted to be within 20% of the measured values.\nIn the next phase, a two-dimensional discrete element model was developed to model single-cell circulation in vibratory beds that had both vertical and horizontal components of motion. The model predictions were compared with experimental measurements of the onset and growth of circulation in beds of steel and glass spheres as a function of bed depth, inter-particle and wall friction coefficients, and the amplitude of vibration. While the values from the DEM showed an error of up to 50% in the predicted circulation strength, depending on the type of the media and system conditions, the trends predicted by the model closely matched those in the experiments. Finally, a physical model was developed to describe the relationship between the onset and direction of circulation with the vibration of the container. A similar model was used to describe the experimental results as well as the transition in circulation patterns in terms of the resultant shear forces at the vibrating container walls and the interlocking of media close to the container walls. It was also demonstrated that a two-dimensional DEM could model a granular flow in which the media had three-dimensional contact and freedom of movement, but that was driven by vibrations in a plane.\nIn summary, it was found that the linear optimization procedure for the contact parameters is an efficient way to improve the results from DEM. Additionally, the circulation in a tub-vibrator increased with the depth of the particulate media in the container, and with the magnitude of the wall-particle and particle-particle friction coefficients. The strength of circulation also increased with the amplitude of vibration. A strong correlation existed between the total shear force along the vibrating container walls and the circulation behavior. Bulk circulation increased sharply when increasing bed depth increased the pressure and the shear forces at the walls and between particle layers. It was also concluded that dimensionless bed depth (the ratio of bed depth to particle diameter) was not a proper dimensionless group when discussing the circulation behavior and it should act in conjunction with other parameters.

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