Contact heating of bi-dispersed milli-beads in a rotary drum. Mechanical segregation impact on temperature distribution and on heating kinetic analyzed by DEM simulation
Graphical abstract
Introduction
Modeling and simulation of processes involving stirred beds of particulate solids is a difficult task. The classical macroscopic and continuous medium approach gives a global scope of average trends but does not provide local information which may be critical for some high added-value processes of pharmaceutical bulk products. In most cases, even slight processing discrepancies between individual particles must be avoided. During drying of granular beds, stirring is very often combined with contact heating and the particulate flow mechanics is then coupled with heat transfer. For instance, vacuum contact heating is widely used in the pharmaceutical industry to dry granular products which are sensitive to oxygen and temperature. The vacuum contact drying of stirred powder bed has been firstly investigated in a macroscopic way (“penetration” model) by Schlünder and Mollekopf [1] for a mono-dispersed and not adhesive granular material. Later, Kwapinska et al. [2] compared the results obtained by the “penetration” analytical method with those obtained by the numerical DEM.
More recently, several authors have independently investigated the effect of operating conditions on mixing and heating rates of rotated beds of monodispersed granular materials. Figueroa et al. [3] have studied various tumbler filling ratios and cross-sectional shapes; Chaudhuri et al. [4] considered various revolution speeds, material types and baffles number and shapes; Gui et al. [5] and Komossa et al. [6] investigated the effect of different revolution speeds; Emady et al. [7] the effect of different revolution speeds and material thermal conductivities; Nafsun et al. [8] considered different revolution speeds and filling ratios. According to this last experimental study, the thermal mixing time, i.e. the time needed for the entire bed composed initially of hot and cold particles to reach a nearly uniform temperature, was decreasing with increasing the rotational speed, or by increasing the number of baffles or by decreasing the filling ratio.
However, industrial materials, even if carefully controlled before processing, are always slightly dispersed in size, or form or composition. Monodispersed beds are textbook reference cases. The major issue industrial R&D engineers are faced with is the transient temperature distribution within dispersed beds composed of particles of different sizes and materials. To our best knowledge, the only publication which dealt directly with thermal dispersion in rotating heterogeneous particulate beds is the second paper of Nafsun et al. [9]. Like in their first paper, the mixing of cold and hot particles was considered, but additionally the influence of different particle size ratio and volume ratio of cold and hot particles was studied. The thermal mixing time was observed to decrease with increasing the particle size for monodispersed beds. Furthermore, in most of the studied bed compositions the thermal mixing times were found to be higher for bi-dispersed beds than for monodispersed ones.
Rotary mixing of imperfectly monodispersed solid particulate beds unavoidably leads to mechanical segregation, i.e. to accumulation of smaller or/and denser particles in the core of the bed [10]. In our parallel study (results not yet published), radial and axial segregations were experimentally observed for a bi-dispersed bed with two particle sizes or with two particle densities. The radial segregation indexes were measured for different drum filling ratios and for different baffles numbers and heights. The axial segregation index was found to be influenced by the friction coefficient on both drum front and rear walls.
In the case of a bed heated by the lateral cylindrical wall of the rotary drum, which was the situation considered in this work, there exist unavoidably a thermal heterogeneity due to the superficial heat supply. Temperature gradients between the bed core and bed periphery will quickly rise up and then slowly fall down. The evolutions of beads temperature depend on their trajectories and especially on the number of contacts with neighboring particles and with the heating wall. If there is spatial material heterogeneity due to mechanical segregation, it may be expected that the thermal heterogeneity will be enhanced or/and extended in time. This is why mechanical segregation may be suspected to induce additional thermal dispersion called in this paper thermal segregation. In order to quantify separately the effect of mechanical segregation from that of the surface heat source on global thermal dispersion within the bed, a specific thermal segregation index was introduced (see Section 2.3) and was used for comparing different morphologies of the bed.
The aim of this paper was first to show the influence of the beds morphologies (mono-dispersed, gaussian-dispersed and bi-dispersed) and baffles configuration (no baffles, short baffles and long baffles) on the thermal homogeneity and global heating kinetic of the bed during mixing and heating inside a rotary drum. Second, the goal was to investigate the impact of mechanical segregation on the thermal dispersion (temperatures heterogeneity) in bi-size and bi-density beds of spherical milli-beads. The analysis was based on DEM simulations of flow and heat transfer in a rotating ‘slice’ type (nearly bi-dimensional) drum.
Section snippets
Theory and methods
The simulations of stirring and contact heating of milli-beads were realized with the commercial software EDEM 2017 (DEM Solutions, Edinburgh, UK). This software is based on the discrete elements method (DEM) which is a very powerful tool used more and more nowadays to investigate and develop granular solid processes. In the DEM framework, each particle of the granular bed is considered to be distinct and has its own trajectory and speed. The particle-particle and particle-boundary interactions
Results and discussion
The simulations were realized for the four types of bed and the three baffles configurations and are summarized in Table 4.
The mechanical segregation index (MSI), the thermal segregation index (TSI), the temperature standard deviation (σT) and the overall bed temperature (〈T〉), defined in Section 2.3, were calculated with MATLAB from EDEM data extracted for each simulation and were plotted as function of time.
The mechanical and thermal distribution of beads at the front face of the bi-size bed
Conclusion
Mechanical flow and heat transfer phenomena within a bed composed of milli-metric size spherical beads rotated and heated by contact in a horizontal drum were investigated. The mechanical segregation index (standard deviation of local bed compositions), the standard deviation of beads temperatures and the thermal segregation index (normalized standard deviation) were calculated by means of the DEM method for four very different types of beds: mono-dispersed, gaussian-dispersed, bi-size and
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