Analysis and modelling of bead contacts in wet-operating stirred media and planetary ball mills with CFD–DEM simulationsby S. Beinert, G. Fragnière, C. Schilde, A. Kwade

Chemical Engineering Science


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Analysis and modelling of bead contacts in wet-operating stirred media and planetary ball mills with CFD–DEM simulations

S. Beinert n, G. Fragnière, C. Schilde, A. Kwade

Institute for Particle Technology, TU Braunschweig, Volkmaroder Strasse 5, 38104 Braunschweig, Germany

H I G H L I G H T S  We investigated the grinding media movement in wet operating mills with CFD–DEM simulations.  The influence of mesh size, steady state and reproducibility were discussed.  An existing analytical model for stirred media mills was compared with the simulative results.  An extended contact analysis was developed (consider impact, torsion, shearing and rolling).  This analysis was used to quantify the contact type for the entire stress energy spectrum. a r t i c l e i n f o

Article history:

Received 18 February 2015

Received in revised form 17 April 2015

Accepted 18 May 2015

Available online 6 June 2015


Coupled CFD–DEM simulations


Contact analysis

Stirred media mills

Planetary ball mills a b s t r a c t

Wet fine grinding is an important unit process in various industries. In the present work two different stirred media mills (one with a cylindrical stirrer; one with a disc stirrer) and a planetary ball mill are investigated using coupled CFD (computational fluid dynamics) and DEM (discrete element method) simulations. While the DEM takes the grinding media into account, the CFD is used for the calculation of the fluid flow. With these coupled simulations the grinding media movement and the resulting contacts per time unit as well as their kinetic energy at the start of the contact can be tracked. In a first step these values are compared to an analytical model that was originally developed for wet operating stirred media mills. To compare different types of mills the type of contact along the stress energy spectrum, which is based on the kinetic energy of the grinding media, is important. Therefore, in the present work an extended contact analysis was developed that enables the description of normal impact and torsion, shearing and rolling induced by rotational and translational velocities. The extended analysis enables the complete characterisation of the energy spectrum for different mill types and operating conditions. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction

Wet fine grinding is an important unit process in mineral, chemical, pharmaceutical, food and paint industries. The movement and collisions of the grinding media in such mills are of major interest in order to model the energy transfer to the product. This information is used to set optimal operation points (Kwade and Schwedes, 2007;

Breitung-Faes and Kwade, 2013), compare and design equipment or to model the grinding process with mechanistic models (see e.g. Tavares and de Carvalho, 2009; de Carvalho and Tavares, 2009; Powell, 2006;

Powell et al., 2008). Next to experimental investigations (see e.g. Van der Westhuizen et al., 2011) the discrete element method is a powerful tool to track grinding media trajectories and collisions in detail. Out of the bead trajectory and collision data stress energy distribution can be calculated and compared with the fracture energy distribution of product particles as for example shown for coarse particle in ball mills by de Carvalho and Tavares (2013). On material side the type of stress influences the breakage behaviour. For example

Tomas (2007, 2009) describes the micro-mechanical behaviour of fine powders by taking four different characteristic stresses into account: normal compression, tangential shearing, rolling and torsion. For those different stresses the load, unloading and reloading paths are discussed with respect to the energy absorption for different material behaviour like elastic–dissipative or elastic–plastic. There is also evidence that the fracture energy of particles depends on the ratio of normal to shear forces in compression stressing (see the work of

Hess, 1980).

This work is the continuation of previous works that aimed to get a better understanding of the grinding media movement and their contact behaviour. In Schilde et al. (2011) and Beinert et al. (2012) an annular gap mill was simulated using the discrete element method (DEM). The effect of the surrounding fluid was included into the

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Chemical Engineering Science 0009-2509/& 2015 Elsevier Ltd. All rights reserved. n Corresponding author. Tel.: þ49 531 391 9621; fax: þ49 531 391 9633.

E-mail address: (S. Beinert).

Chemical Engineering Science 134 (2015) 648–662 contact model. These simulations already enabled a rough estimation of particle breakage. In a second step the same mill was simulated with coupled simulations and compared with dry particle simulations with or without a modified contact model (see Beinert et al., 2014).

Additionally, these results were linked with micro-compression tests of aggregates to describe the breakage of those aggregates in the investigated mill and model the progress of the median particle size distribution over time.

In the present paper three mills are examined with coupled

CFD (computational fluid dynamics) and DEM simulations for different process parameters. The results are compared to an analytical model (stress energy model described in Kwade and

Schwedes, 2007). Additionally, the types of contacts are quantified with the developed extended contact analysis. 1.1. Simulations of mills and particle movement

Weerasekara et al. (2013) reviewed DEM applications in comminution research and the use of the simulation data in process models. To improve ball mills the discrete element method is an optimal method due to the possibility of tracking the grinding media and their collisions. Cleary (1998) used the DEM to simulate the particle flow inside an autogenous ball mill for varying particle sizes and densities while interacting with complex geometries. The charge behaviour, torque and power draw were used to analyse the effect of the coefficients of friction and restitution. Furthermore, he investigated the effect of size segregation as well as wear and used the simulations to improve the geometry of the liner to reduce wear. The effect of contact mechanic and the application of the DEM for different industries are shown in Mishra (2003a,b). In wet operated mills the influence of the fluid has to be taken into account. This can be done by computational fluid dynamics (see e.g. Jayasundara et al., 2011 or