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285352 Axial Mixing of Polypropylene Particles in Horizontal Rotating Drum Mixers

Axial mixture characterization is a widespread problem in granular particle blending processes (Wightman et al., 1996) such as in an horizontal rotating drum mixer. In such a configuration, homogeneous mixture of particles is desired by blending the particles via rotating paddles in a fixed cylindrical drum. This problem, also common to many other technological devices (Khan et al, 2011), is adversely reflected in the manufacture of a broad variety of industrial products, such as polypropylene. The numerical study of such granular flow configurations receives increasing academic and industrial attention, however, the granular flow behavior in these systems is still poorly understood.

In this work, characterization of the axial mixture of experimental configuration of the granular flows in a pilot-scale horizontal cylindrical particle drum mixer is numerically studied. The simulations are performed using an Euler-Euler code called ‘NEPTUNE_CFD’ in a rotational frame of reference with additional terms accounting for the centrifugal and Coriolis forces in the momentum equation. The k-epsilon model treats the turbulence of the fluid phase and the agitation of the particle phase is treated using the kinetic theory approach for the turbulent stresses (Simonin, 2000). This kinetic theory approach for the motion of the particles, considering particle-particle collisions, is theoretically inadequate for the granular flows where the particle-particle interaction durations are long and the transfer of momentum between the particles is dominated by the frictional forces. These frictional interactions are taken into account by a stress tensor added to the viscous stress tensor in the context of the model proposed by Srivatava and Sundaresan (2003) for the quasi-static granular flows. This model is largely empirical and widely used in critical state soil mechanics research.

Our results show that the paddle shape has a primordial effect on the axial mixing of the particles. Besides, we also observed that the angular velocity of rotation of paddles has a slight effect on the axial mixing whereas the initial fill of the cylinder practically does not have any effect on the mixing. To characterize the mixing, a convective velocity has been calculated by considering the axial transport of a passive scalar. Calculation of the axial passive scalar gradient led us to determine a dispersion coefficient to evaluate the nature of the flows. Although these methods permit us to determine the nature of the flow, a still more robust method to fully characterize the axial mixing is an open problem. Nevertheless, our qualitative comparisons with the experimental results are in coherence. For the future prospects, after the completion of comparison of our results with the experimental ones, our ongoing research will be on the more realistic representation of the industrial scale geometry and the process of the polypropylene production. The sensibility of the simulations to the frictional viscosity model parameters will also be clarified in our future study.

**References**

Khan, Z. S., Van Bussel, F., Schaber, M., Seemann, R., Scheel, M., and Di Michiel, M., *High-speed measurement of axial grain transport in a rotating drum, New Journal of Physics, 13, 105005.*

Simonin, O., *Statistical and continuum modelling of turbulent reactive particulate flows. part 1: theoretical derivation of dispersed eulerian modelling from probability density function kinetic equation.*In Lecture Series 2000-06. von Karman Institute for Fluid Dynamics, 2000.

Srivastava, A. and Sundaresan, S., *Analysis of a frictional–kinetic model for gas–particle flow*, Powder Technology, 129, p72-85, 2003

Wightman, C., J. Muzzio, F., Wilder, J., *Quantitative image analysis method for characterizing mixtures of granular materials, Powder Technology, 89, 165-176, 1996*

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