Computational Modelling

Granular Flow - Application

Charge motion in a centrifugal mill with various loadings

Contact personnel:  P.W. Cleary

The charge in a 30 cm centrifugal mill, used for high intensity and ultra-fine grinding, has been investigated. The cylinder executes a centrifugal motion with diameter 12 cm. The supporting arm rotates at 1000 rpm while the mill cylinder counter-rotates at the same rate. It is filled with uniform 6 mm particles and there are four flat lifters. These parameters were chosen to match the experimental configuration used by Hoyer [1]. The particle distributions, both measured experimentally and predicted by the DEM simulations, are shown below for three different particle loadings.

Experiment	DEM simulation
		75% charge
		50% charge
		25% charge

It can be observed that the numerically-predicted charge profiles show very close agreement with the high-speed photographs of Hoyer. The 75% and 50% loaded cases exhibit a steady stable charge profile that simply rotates with the mill whilst the granular material deformed smoothly. This is in accordance with the behaviour observed experimentally. Furthermore, the charge profiles matched the experiments very closely, with the 75% case being indistinguishable even to the point of predicting the same amount between the lifter and the charge as the charge separate the lifter at the top.

Theoretically there is a complete change in the flow behaviour for loads less than 30%. This also observed experimentally. The simulation of the 25% loaded case exhibits the same unsteady flow as the experiments with the particles forming a characteristic distorted three pointed shape that flops around the the inside of the mill with a tumbling motion spraying loose particles all around.

Power measurements were also made by Hoyer [2] for the centrifugal mill with a fill level of 40% and a charge consisting of 4 kg of steel balls and 1 kg of quartz for a range of rotation rates. Matching DEM simulations were performed to determine the accuracy of the DEM predictions. The figure below shows the experimental, theoretical (also from Hoyer [2]) and DEM results for various rotation rates. The power predictions are all normalised by the mass of the charge to give specific power consumption, in order to enable direct comparison of these quantities. For most mill speeds multiple power measurements were made. They show a reasonable amount of variation. The spread in these results provides some idea of the amount of experimental error or variation that is intrinsic to these systems. The precise reasons for these variations are unknown.

Comparison of power calculated from DEM simulations (circles) with experimental measurements (crosses) and theoretical predictions (triangles).

For 300 rpm, the DEM prediction is extremely close to the single experimental result and is closer than the theoretical one. For the higher rotation rates (for which multiple experimental measurements were made) all the DEM predictions lie well within the experimental ranges. In general, they are near the middle of the ranges and for the 400 rpm case the DEM result is in the lower part of the range. One would expect the DEM predictions to be slightly lower than the true power consumption because mechanical energy losses in the motor and gears of the mill are not included in these predictions. The DEM power consumption is purely that consumed by the actual particle motions and their interactions with the mill chamber. It is also clear from this figure that the theoretical predictions of Hoyer [2] represent an upper bound for the power, corresponding to the upper limit of the experimental range for each rotation rate. The DEM predictions are much closer to the mean experimental power for each rotation rate than are the theoretical values. This suggests that DEM is likely to give a good estimate of actual power draw and will predict this more accurately than does the theory.

This is one of the few applications for which we have been able to obtain high quality experimental data. The very close agreement between the simulations, the experiments and with the theory gives us a degree of confidence that the DEM approach of trying to model correctly the applications at the particle level is capturing sufficient reality to give good predictions. One important caveat is that the particles used in the experiments were very close to spherical and so the circular particles used to model them are a good approximation. Cases where the real particles are really non-circular are not always well matched by DEM simulations using circular particles. Flows such as in hoppers and in slowly rotating tumblers where the material is partially stationary and then must shear can be significantly affected by ignoring particle shape.

More details regarding this application can be found in [3].

References

[1] D.I. Hoyer, Particle trajectories and charge shapes in centrifugal mills, Proceedings of the International Conference on Recent Advances in Mineral Sciences and Technology, MINTEK, South Africa, pp.401-409 (1984).

[2] D.I. Hoyer, A study of the behaviour of the centrifugal ball mill, Ph.D. Thesis, University of Natal, South Africa (1985).

[3] P.W. Cleary and D. Hoyer, Centrifugal mill charge motion: comparison of DEM predictions with experiment, accepted for publication in International Journal of Mineral Processing (1999).

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last updated July 18, 2007 05:24 PM

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