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Abstract:
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The current study is aimed at the development of a theoretical
simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics
of solid bed in the cross section of the horizontal rotating cylinder at the microscopic
level and subsequently apply this model to establish the transition behaviour, mixing and
segregation.The simulation of the granular motion developed in this work is based on solving
Newton's equation of motion for each particle in the granular bed subjected to the
collisional forces, external forces and boundary forces. At every instant of time, the
forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After
checking the validity of the code with special tests, it is used to investigate the transition
behaviour of granular solids motion in the cross section of a rotating cylinder for various
rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete
Element Method (DEM) of the motion of granular solids in the radial direction of the
horizontal cylinder to elucidate the relationship between the operating parameters of the
rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational
velocities of the cylinder and volumetric fill. The physical properties of the granular
solids include particle sizes, densities, stiffness coefficients, and coefficient of friction
Further the work highlights the fundamental basis for the important phenomena of the
system namely; (i) the different modes of solids motion observed in a transverse crosssection
of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the
granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the
transition behaviour in terms of the bed turnover time and rotational speed and (iv) the
segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the
granular solid bed is quantified in terms of Froude number and the results obtained are
validated with experimental and theoretical results reported in the literature The
transition from slumping to rolling mode is quantified using the bed turnover time and a
linear relationship is established between the bed turn over time and the inverse of the
rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the
rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose
are presented and discussed. The variation of active layer depth with respect to fill
fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at.
[2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and
segregation in the transverse direction for different particle sizes and their size ratios. The
effect of fill fraction and rotational speed on the transverse mixing behaviour is presented
in the form of a mixing index and mixing kinetics curve. The segregation pattern
obtained by the simulation of the granular solid bed with respect to the rotational speed of
the cylinder is presented both in graphical and numerical forms. The segregation
behaviour of the granular solid bed with respect to particle size, density and volume
fraction of particle size has been investigated. Several important macro parameters
characterising segregation such as mixing index, percolation index and segregation index
have been derived from the simulation tool based on first principles developed in this
work. |