(41d) Dynamics and Energetics for a Vertically Stirred Mill: Validation of a Discrete Element Method (DEM) Model Via Positron Emission Particle Tracking (PEPT)
Dynamics and Energetics for a Vertically Stirred Mill: validation of a Discrete Element Method (DEM) Model via Positron Emission Particle Tracking (PEPT).
Domenico Daraio**, Hugh E. Stitt * Alessio Alexiadis **, Andrew Ingram**, and Michele Marigo *
* Johnson Matthey Technology Centre - Chilton Site - Billingham (UK)
** School of Chemical Engineering - University of Birmingham â Birmingham â (UK)
e-mail: Domenico.daraio @matthey.com,
Vertically stirred attritor mills are widely used for comminution in numerous industrial applications ranging from the ceramics, paint, pharmaceutical and mineral industries. This type of mill can be utilised for both dry or wet milling in order to achieve ultrafine grinding.
The comminution energy is transferred by a motor driven impeller to the grinding media to achieve the wanted particle size reduction. Unfortunately, not all the energy is effectively used in the reduction process of the product, a large part of it is dissipated by energy loss during the collisions and friction among the grinding media, in the forms of heat and noise. The full understanding for both the media motion and the media ball-media ball, media ball-impeller and media ball-grinding chamber interactions are the key features that need to be analysed in order to improve the efficiency of the equipment and/or the product quality. In addition, often the design and the scale-up are developed on an empirical basis due to the lack of understanding of how the energy is really transferred from the grinding media to the powder and what are the dominant mechanisms for the media motion.
The current work addresses these limitations with a more mechanistic approach, adopting the Discrete Element Method (DEM LIGGGHTS, by DCS computing, Linz -Austria), to reveal the exchange of stresses and force distribution during the milling operation under a variety of conditions (impeller speed, media filling, shaft design, impeller configuration). Positron Emission Particle Tracking measurements, a non-invasive technique, has been utilised for model validation by investigating the grinding beads dynamics inside a 1.4lt lab attritor mill under similar conditions to the DEM model. A Matlab routing has been adapted and modified to fit the specific case, to produce azimuthally averaged velocity and occupancy distributions of the PEPT data.
A sensitivity study has been carried out for four DEM input parameters describing the particle properties (Youngâs Modulus, static friction coefficient, rolling friction coefficient, coefficient of restitution) using a matrix of simulations according to the principle of the Design of Simulations (DoS). 16 simulations were necessary to understand the role of each parameter and their impact on the simulation results was assessed against two responses: the power consumption coming from the experiments (global validation of the DEM model) and the local velocity calculated using the PEPT raw data (local validation of the DEM model).
It has been found that the frequency distribution of velocity obtained from the PEPT experiments, (tracking a single particle for an extended time), is not equivalent to the DEM-velocity distribution based on the entire particle population. However, the DEM model is capable of capturing the main features of the grinding media motion in term of torque on the impeller and velocity of the particles. In fact, the DEM model predicts well the local grinding media velocity at different radial positions along the attritor mill height, allowing more trustful considerations on the collision energetics. Inside the attritor mill have been identified and classified four distinct area where the particle motion is controlled by different mechanisms: rolling and/or static friction between layers of particles, gravity, impacts between the particles. More important the extension of these area will affect the efficiency of the equipment and /or product quality. Combining the information of the residence time and the particle velocity, the death area inside the equipment have been mapped and they have been minimised by optimising the impeller configuration.
For a more quantitative evaluation of the different milling conditions, the DEM data have been time and space averaged using a novel coarse-graining post-processing tool (Particles Analytics Ltd, Edinburgh, UK). Continuous fields of velocity, kinetic pressure, solid fraction and number of contacts were computed and used as starting point for a re-design of the impeller.
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