Agba D. Salman

AN EXPERIMENTAL STUDY OF THE ELASTIC REBOUND OF SPHERES

Abstract Accurate measurements have been made of the impact and rebound behaviour of 5-mm aluminium oxide spheres impacting a thick soda–lime glass anvil, for impact angles from normal to very near glancing incidence. Speed, angle and rotation before and after impact have been measured with a strobe and single-frame digital camera. Reproducibility and precision are considerably better than in any previously published work, and have been achieved by careful attention to all aspects of the experiment, including the mechanical and optical systems, illumination, electronic control, computer-based image measurement, and the geometry and condition of the impacting surfaces. All aspects of the rebound dynamics of the elastic spheres, including the motion of the centre of mass and of the contact patch, the spin and the partition of energy, are fully described by the measured variation of the normal and tangential restitution coefficients over the range of impact angles. These measurements show very close agreement with the numerical work of Maw et al. which takes into account the effects of sticking, microslip and tangential compliance. For impacts with a greater obliqueness than about 30° from the normal, the results also agree closely with the classical theory of rigid body sliding.

An experimental investigation of particle fragmentation using single particle impact studies

This paper presents the results of a comprehensive programme of experiments in which particles were impacted under controlled conditions against solid targets. The overall aim of these experiments was to gain an understanding of the fragmentation process of particle products in a pneumatic conveying system. A continuous air gun was used to examine the effect of particle velocity, impact angle, particle diameter, target material, target thickness and number of impacts on the fragmentation of spherical aluminium oxide particles. The effect of the impact velocity on the fragment size distribution was also examined. The results showed that decreasing the impact velocity, impact angle, target thickness, target hardness and particle size decreased the fragmentation rate. Quantifying the effect of these variables on particle fragmentation provides further understanding of how particles behave during pneumatic conveying, especially in terms of conveying velocities, bend geometry and bend surface material.

Accurate measurement of particle impact parameters

The aim of this paper is to describe an experimental facility to measure the low velocity impact behaviour of spherical particles with high accuracy. Measurements have been made of particle rotation, normal restitution coefficient to within of glancing incidence, and tangential restitution coefficient to within of normal impact, with very low scatter. The results are accurate enough to be used for quantitative comparison to theoretical studies. Achievement of a high level of precision and reproducibility has involved detailed attention to all aspects of the experiment design, construction, control and computer-based image measurement.

Coupling granule properties and granulation rates in high-shear granulation

It is possible to link granulation rates to granule properties. The linkage is by multiple dimension population balance equations that, by means of simplifying assumptions, can be reduced to multiple one-dimensional (1-D) population balance equations (PBEs). Using simple physically based models, this paper demonstrates how multiple one-dimensional population balance equations can describe the results of high-shear granulation experiments of two different materials, calcium carbonate and lactose. Good agreement between experimental and simulated results was achieved enabling the granulation rates to be defined by two model parameters: the critical binder volume fraction and the aggregation rate constant. The modelling framework presented in this paper also provides a basis for the kinetic analysis of granulation experiments so that with further work, it is possible to determine the effect of process conditions and material properties on the model parameters.

Twin screw granulation: steps in granule growth.

The present work focuses on the study of the progression of granules in different compartments along the length of screws in a twin screw granulator (TSG). The effects of varying powder feed rate; liquid to solid ratio and viscosity of granulation liquid on properties of granules was studied. The bigger granules produced at the start of the process were found to change in terms of size, shape and strength along the screw length at all the conditions investigated. The granules became more spherical and their strength increased along the screw length. Tracer granules were also introduced in order to understand the role of kneading and conveying elements in the TSG. The kneading elements promoted consolidation and breakage while the conveying elements led to coalescence, breakage and some consolidation. The results presented here help to provide a qualitative and quantitative understanding of the twin screw granulation process.

A study of solid particle failure under normal and oblique impact

Systematic data is presented on the failure probability of 5.15 mm aluminium oxide spheres over a wide range of impact speed and angle. The high number of tests made, with 100 particles individually tested per data point, was necessary to average out the variations in individual particle properties and to make the results consistent. This has enabled very close curve fits to be made to the data, and the parameters from these fits provide a comprehensive and reliable summary of the material performance. The results show that the probability of particle failure varies only slightly from normal impact to about 50°. Detailed examination of damaged particles has identified four primary forms of fracture which are common to normal impact and static compression. These fractures initiate from a subsurface cone of compression damage, and develop along meridian planes. An additional form of fracture found with oblique impact appears to be a result of tangential loading causing enhanced tension in the surface.

Particle fragmentation in dilute phase pneumatic conveying

Using a continuous-flow gas gun, single particle impact studies were conducted to examine the characteristics of particle fragmentation. The effect of particle velocity, impact angle, particle size and number of impacts on the percentage of unbroken particles was investigated. A numerical simulation, combining particle trajectory with particle fragmentation characteristics was also developed to calculate the percentage of unbroken particles in a horizontal pipe and bend for the case of dilute phase pneumatic conveying. Validation of this model showed good agreement with the simulated and experimental results. The flexibility of this model will also enable particle breakage for any dilute pneumatic conveying configuration to be predicted.

Impact breakage of fertiliser granules

Abstract Systematic data are presented for the single impact failure of 3.2, 5.3, and 7.2 mm fertiliser granules over a wide range of impact speeds and angles. The probability of failure was found to change only slowly between 90° (normal) impact and 50°, but decreased rapidly below 50°. The probability of failure increased with increasing size of granules. The effect of impact velocity on the mean, median and the proportion of the largest-sized fragments were examined. Two distinct forms of normal impact damage were identified, corresponding to low and high impact velocities, and the mechanisms of failure are discussed.

The fracture of glass spheres

Abstract Impact and compression tests have been carried out on soda–lime glass spheres in the diameter range of 0.4–12.7 mm. The paper describes the forms of failure and their variation with diameter and with impact velocity. At the lowest velocities, fractures are mainly due to a brittle–elastic response, with typical Hertzian ring and cone crack systems. At higher velocities or loads, inelastic deformation (densification, flow, or intense local fracturing and crushing) under the impact site leads to characteristic patterns of fragmentation arising from radial, lateral and median cracks.

Drag correlations for particles of regular shape

Abstract Explicit equations are developed to characterize the effects of sphericity and Reynolds number of a particle on its drag coefficient. Experimental data are obtained from a wide range of sources, embracing various shapes including spheres, cube octahedrons, octahedrons, cubes, tetrahedrons, discs, cylinders, rectangular parallelepipeds and others. All these data are grouped within certain ranges of physical and kinematic conditions; sphericity range of 0.006-1 and Reynolds number range of 10 −2 to 10 5 . From the tabulations, equations for drag coefficient are developed and proposed based on the Kaskas equation. The constants in the equations are determined by the least-squares method and the calculated overall accuracy is approximately 97%. Manipulation of the constants allows three respective general equations to be proposed. Using these equations, prediction of drag coefficient of a particle based on its sphericity and Reynolds number would be simpler, easier and faster.